On the Number of Rational Points on Prym Varieties over Finite Fields
Aubry, Yves; Haloui, Safia
2016-01-01
We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.......We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2....
Rational points on elliptic curves
Silverman, Joseph H
2015-01-01
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and ...
Counting rational points on cubic curves
HEATH-BROWN; Roger; TESTA; Damiano
2010-01-01
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals.The bounds are uniform in the curve and involve the rank of the corresponding Jacobian.The method used in the proof is a combination of the "determinant method" with an m-descent on the curve.
On Counting the Rational Numbers
Almada, Carlos
2010-01-01
In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…
The relational nature of rational numbers
Bruce Brown
2015-06-01
Full Text Available It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children’s difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers.
On curves over finite fields with many rational points
Fuhrmann, R; Fuhrmann, Rainer; Torres, Fernando
1996-01-01
We study arithmetical and geometrical properties of {\\it maximal curves}, that is, curves defined over the finite field \\mathbb F_{q^2} whose number of \\mathbb F_{q^2}-rational points reachs the Hasse-Weil upper bound. Under a hypothesis on non-gaps at rational points we prove that maximal curves are \\mathbb F_{q^2}-isomorphic to y^q+y=x^m for some m\\in \\mathbb Z^+.
Patterns in rational base number systems
Morgenbesser, Johannes F; Thuswaldner, Jörg
2012-01-01
Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\\'ele ring $\\mathbb{A}_\\mathbb{Q}$ and Fourier analysis in $\\mathbb{A}_\\mathbb{Q}$. With help of these tools we are able to reformulate our results as ...
A REMARK ON IMPLICITIZING RATIONAL CURVES WITH BASE POINTS
CHENFALAI
1998-01-01
A simple relationship between the Bezout matrix corresponding to a rational curve with base points and the Bezout matrix corresponding to the same rational curve except that whose base points are eliminated is clarified. Based on this relationship,the author proves that the implicit equation of a rational curve with base points is the largest rton-zero leading principal minor of the gezout resultant corresponding to the rational curve assuming that the rational curve doesn't have triva/base point 0,and thus provides a simple approach to Jmplicitze rational curves with base points. Furthermore，as a by-product ，art algorithm is presented to compute the base points of a rational curve.
Early Developmental Trajectories toward Concepts of Rational Numbers
Kainulainen, Mikko; McMullen, Jake; Lehtinen, Erno
2017-01-01
Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…
Relational Reasoning with Rational Numbers: Developmental and Neuroimaging Approaches
DeWolf, Melissa
2016-01-01
The study of how children and adults learn mathematics has given rise to a rich set of psychological phenomena involving mental representation, conceptual understanding, working memory, relational reasoning and problem solving. The subfield of understanding rational number processing and reasoning focuses on mental representation and conceptual understanding of rational numbers, and in particular fractions. Fractions differ from other number types, such as whole numbers, both conceptually a...
Quaternion Algebras over Curves of Genus One Without Rational Points
Susanne Pumpl(u)n
2005-01-01
Quaternion algebras over curves of genus one without rational points over perfect fields of characteristic not two are classified. As a consequence, all quaternion algebras over the function field of such a curve, which are unramified everywhere, are classified.
Cubic Polynomials with Rational Roots and Critical Points
Gupta, Shiv K.; Szymanski, Waclaw
2010-01-01
If you want your students to graph a cubic polynomial, it is best to give them one with rational roots and critical points. In this paper, we describe completely all such cubics and explain how to generate them.
Erich Selder
2015-01-01
Full Text Available The correspondence between right triangles with rational sides, triplets of rational squares in arithmetic succession and integral solutions of certain quadratic forms is well-known. We show how this correspondence can be extended to the generalized notions of rational θ-triangles, rational squares occurring in arithmetic progressions and concordant forms. In our approach we establish one-to-one mappings to rational points on certain elliptic curves and examine in detail the role of solutions of the θ-congruent number problem and the concordant form problem associated with nontrivial torsion points on the corresponding elliptic curves. This approach allows us to combine and extend some disjoint results obtained by a number of authors, to clarify some statements in the literature and to answer some hitherto open questions.
Rational points, rational curves, and entire holomorphic curves on projective varieties
Gasbarri, Carlo; Roth, Mike; Tschinkel, Yuri
2015-01-01
This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation.
Some fixed point results for dualistic rational contractions
Muhammad Nazam
2016-10-01
Full Text Available In this paper, we introduce a new contraction called dualistic contraction of rational type and obtain some fixed point results. These results generalize various comparable results appeared in the literature. We provide an example to show the superiority of our results over corresponding fixed point results proved in metric spaces.
A Collatz-type conjecture on the set of rational numbers
Javaheri, Mohammad
2010-01-01
Define $\\theta(x)=(x-1)/3$ if $x\\geq 1$, and $\\theta(x)=2x/(1-x)$ if $x<1$. We conjecture that the orbit of every positive rational number ends in 0. In particular, there does not exist any positive rational fixed point for a map in the semigroup $\\Omega$ generated by the maps $3x+1$ and $x/(x+2)$. In this paper, we prove that the asymptotic density of the set of elements in $\\Omega$ that have rational fixed points is zero.
Rational numbers with purely periodic $\\beta$-expansion
Adamczewski, Boris; Siegel, Anne; Steiner, Wolfgang
2009-01-01
We study real numbers $\\beta$ with the curious property that the $\\beta$-expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numbers have to be Pisot numbers which are units of the number field they generate. We complete known results due to Akiyama to characterize algebraic numbers of degree 3 that enjoy this property. This extends results previously obtained in the case of degree 2 by K. Schmidt, Hama and Imahashi. Let $\\gamma(\\beta)$ denote the supremum of the real numbers $c$ in $(0,1)$ such that all positive rational numbers less than $c$ have a purely periodic $\\beta$-expansion. We prove that $\\gamma(\\beta)$ is irrational for a class of cubic Pisot units that contains the smallest Pisot number $\\eta$. This result is motivated by the observation of Akiyama and Scheicher that $\\gamma(\\eta)=0.666 666 666 086 ...$ is surprisingly close to 2/3.
Floating point numbers are real numbers
Mascarenhas, Walter F.
2016-01-01
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which continuous mathematics leads to sharp, simple and new results about the evaluation of sums, square roots and dot products in floating point arithmetic.
Repelling periodic points of given periods of rational functions
CHANG Jianming; FANG Mingliang
2006-01-01
Let R(z) be a rational function of degree d ≥ 2. Then R(z) has at least one repelling periodic point of given period k ≥ 2, unless k = 4 and d=2, or k= 3 and d ≤ 3, or k=2 and d≤8. Examples show that all exceptional cases occur.
Neural representations of magnitude for natural and rational numbers.
DeWolf, Melissa; Chiang, Jeffrey N; Bassok, Miriam; Holyoak, Keith J; Monti, Martin M
2016-11-01
Humans have developed multiple symbolic representations for numbers, including natural numbers (positive integers) as well as rational numbers (both fractions and decimals). Despite a considerable body of behavioral and neuroimaging research, it is currently unknown whether different notations map onto a single, fully abstract, magnitude code, or whether separate representations exist for specific number types (e.g., natural versus rational) or number representations (e.g., base-10 versus fractions). We address this question by comparing brain metabolic response during a magnitude comparison task involving (on different trials) integers, decimals, and fractions. Univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically, within the intraparietal sulcus, from that of both decimals and integers, while the latter two number representations appeared virtually indistinguishable. These results demonstrate that the two major notations formats for rational numbers, fractions and decimals, evoke distinct neural representations of magnitude, with decimals representations being more closely linked to those of integers than to those of magnitude-equivalent fractions. Our findings thus suggest that number representation (base-10 versus fractions) is an important organizational principle for the neural substrate underlying mathematical cognition.
Reasoning strategies with rational numbers revealed by eye tracking.
Plummer, Patrick; DeWolf, Melissa; Bassok, Miriam; Gordon, Peter C; Holyoak, Keith J
2017-07-01
Recent research has begun to investigate the impact of different formats for rational numbers on the processes by which people make relational judgments about quantitative relations. DeWolf, Bassok, and Holyoak (Journal of Experimental Psychology: General, 144(1), 127-150, 2015) found that accuracy on a relation identification task was highest when fractions were presented with countable sets, whereas accuracy was relatively low for all conditions where decimals were presented. However, it is unclear what processing strategies underlie these disparities in accuracy. We report an experiment that used eye-tracking methods to externalize the strategies that are evoked by different types of rational numbers for different types of quantities (discrete vs. continuous). Results showed that eye-movement behavior during the task was jointly determined by image and number format. Discrete images elicited a counting strategy for both fractions and decimals, but this strategy led to higher accuracy only for fractions. Continuous images encouraged magnitude estimation and comparison, but to a greater degree for decimals than fractions. This strategy led to decreased accuracy for both number formats. By analyzing participants' eye movements when they viewed a relational context and made decisions, we were able to obtain an externalized representation of the strategic choices evoked by different ontological types of entities and different types of rational numbers. Our findings using eye-tracking measures enable us to go beyond previous studies based on accuracy data alone, demonstrating that quantitative properties of images and the different formats for rational numbers jointly influence strategies that generate eye-movement behavior.
Elementary Teacher Candidates’ Understanding of Rational Numbers: An International Perspective
Carbone, Rose Elaine
2012-01-01
This paper combines data from two different international research studies that used problem posing in analyzing elementary teacher candidates’ understanding of rational numbers. In 2007, a mathematics educator from the United States and a mathematician from Northern Ireland collaborated to investigate their respective elementary teacher candidates’ understanding of addition and division of fractions. A year later, the same US mathematics educator collaborated with a mathematics educator from...
Interpretation of human pointing by African elephants: generalisation and rationality.
Smet, Anna F; Byrne, Richard W
2014-11-01
Factors influencing the abilities of different animals to use cooperative social cues from humans are still unclear, in spite of long-standing interest in the topic. One of the few species that have been found successful at using human pointing is the African elephant (Loxodonta africana); despite few opportunities for learning about pointing, elephants follow a pointing gesture in an object-choice task, even when the pointing signal and experimenter's body position are in conflict, and when the gesture itself is visually subtle. Here, we show that the success of captive African elephants at using human pointing is not restricted to situations where the pointing signal is sustained until the time of choice: elephants followed human pointing even when the pointing gesture was withdrawn before they had responded to it. Furthermore, elephants rapidly generalised their response to a type of social cue they were unlikely to have seen before: pointing with the foot. However, unlike young children, they showed no sign of evaluating the 'rationality' of this novel pointing gesture according to its visual context: that is, whether the experimenter's hands were occupied or not.
Magnitude comparison with different types of rational numbers.
DeWolf, Melissa; Grounds, Margaret A; Bassok, Miriam; Holyoak, Keith J
2014-02-01
An important issue in understanding mathematical cognition involves the similarities and differences between the magnitude representations associated with various types of rational numbers. For single-digit integers, evidence indicates that magnitudes are represented as analog values on a mental number line, such that magnitude comparisons are made more quickly and accurately as the numerical distance between numbers increases (the distance effect). Evidence concerning a distance effect for compositional numbers (e.g., multidigit whole numbers, fractions and decimals) is mixed. We compared the patterns of response times and errors for college students in magnitude comparison tasks across closely matched sets of rational numbers (e.g., 22/37, 0.595, 595). In Experiment 1, a distance effect was found for both fractions and decimals, but response times were dramatically slower for fractions than for decimals. Experiments 2 and 3 compared performance across fractions, decimals, and 3-digit integers. Response patterns for decimals and integers were extremely similar but, as in Experiment 1, magnitude comparisons based on fractions were dramatically slower, even when the decimals varied in precision (i.e., number of place digits) and could not be compared in the same way as multidigit integers (Experiment 3). Our findings indicate that comparisons of all three types of numbers exhibit a distance effect, but that processing often involves strategic focus on components of numbers. Fractions impose an especially high processing burden due to their bipartite (a/b) structure. In contrast to the other number types, the magnitude values associated with fractions appear to be less precise, and more dependent on explicit calculation.
Rational and algebraic approximations of algebraic numbers and their application
袁平之
1997-01-01
Effective rational and algebraic approximations of a large class of algebraic numbers are obtained by Thue-Siegel’s method.As an application of this result,it is proved that; if D>0 is not a square,and ε=x0 +y0 D denotes the fundamental solution of x2-Dy2=-1,then x2+1=Dy4 is solvable if and only if y0=A2 where A is an integer.Moreover,if ≥64,then x2+1=Dy4 has at most one positive integral solution (x,y).
Many rational points coding theory and algebraic geometry
Hurt, Norman E
2003-01-01
This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators.
McMullen, Jake; Hannula-Sormunen, Minna M.; Lehtinen, Erno
2015-01-01
Recent evidence suggests that early natural number knowledge is a predictor of later rational number conceptual knowledge, even though students' difficulties with rational numbers have also been explained by the overuse of natural number concepts--often referred to as the natural number bias. Hannula and Lehtinen ("Learn Instr"…
Genetic Algorithms, Floating Point Numbers and Applications
Hardy, Yorick; Steeb, Willi-Hans; Stoop, Ruedi
The core in most genetic algorithms is the bitwise manipulations of bit strings. We show that one can directly manipulate the bits in floating point numbers. This means the main bitwise operations in genetic algorithm mutations and crossings are directly done inside the floating point number. Thus the interval under consideration does not need to be known in advance. For applications, we consider the roots of polynomials and finding solutions of linear equations.
Bounding the number of rational places using Weierstrass semigroups
Geil, Hans Olav; Matsumoto, Ryutaroh
2007-01-01
Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over Fq in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function field can possibly have and we derive...... an upper bound in terms of the generators of Lambda and q. Our bound is an improvement to Lewittes' bound in [6] which takes into account only the multiplicity of Lambda and q. From the new bound we derive significant improvements to Serre's upper bound in the cases q = 2, 3 and 4. We finally show...
Constructing rational maps with cluster points using the mating operation
Sharland, Thomas
2011-01-01
In this article, we show that all admissible rational maps with fixed or period two cluster cycles can be constructed by the mating of polynomials. We also investigate the polynomials which make up the matings that construct these rational maps. In the one cluster case, one of the polynomials must be an $n$-rabbit and in the two cluster case, one of the maps must be either $f$, a "double rabbit", or $g$, a secondary map which lies in the wake of the double rabbit $f$. There is also a very simple combinatorial way of classifiying the maps which must partner the aforementioned polynomials to create rational maps with cluster cycles. Finally, we also investigate the multiplicities of the shared matings arising from the matings in the paper.
Distribution of rational points of bounded height on equivariant compactifications of PGL 2 I
Takloo-Bighash, Ramin; Tanimoto, Sho
2016-01-01
We study the distribution of rational points of bounded height on a one-sided equivariant compactification of PGL2 using automorphic representation theory of PGL2.......We study the distribution of rational points of bounded height on a one-sided equivariant compactification of PGL2 using automorphic representation theory of PGL2....
van Hoof, Jo; Verschaffel, Lieven; van Dooren, Wim
2015-01-01
The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the…
Clarke, Carne; Fisher, William; Marks, Rick; Ross, Sharon; Zbiek, Rose Mary
2010-01-01
This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…
Arithmetic Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, known as arbitrary precision arithmetic. The assignment asks students to investigate the validity of floating point number precision and the approach of calculating the exact value of a large number, using the basic scientific programming language Fortran. Examples of the successive multiplication of even number and the multiplication and division of two overflowing floats are presented. The application of the scheme to hardware and firmware design which requires the allocation of finite memory, as in a digital signal proce...
Common Fixed Point Theorem in Cone Metric Space for Rational Contractions
R. Uthayakumar
2013-09-01
Full Text Available In this paper we prove the common fixed point theorem in cone metric space for rational expression in normal cone setting. Our results generalize the main result of Jaggi [10] and Dass, Gupta [11].
A rational analysis of the approximate number system.
Piantadosi, Steven T
2016-06-01
It is well-known in numerical cognition that higher numbers are represented with less absolute fidelity than lower numbers, often formalized as a logarithmic mapping. Previous derivations of this psychological law have worked by assuming that relative change in physical magnitude is the key psychologically-relevant measure (Fechner, 1860; Sun et al., 2012; Portugal & Svaiter, Minds and Machines, 21(1), 73-81, 2011). Ideally, however, this property of psychological scales would be derived from more general, independent principles. This paper shows that a logarithmic number line is the one which minimizes the error between input and representation relative to the probability that subjects would need to represent each number. This need probability is measured here through natural language and matches the form of need probabilities found in other literatures. The derivation does not presuppose anything like Weber's law and makes minimal assumptions about both the nature of internal representations and the form of the mapping. More generally, the results prove in a general setting that the optimal psychological scale will change with the square root of the probability of each input. For stimuli that follow a power-law need distribution this approach recovers either a logarithmic or power-law psychophysical mapping (Stevens, 1957, 1961, 1975).
A systematic investigation of the link between rational number processing and algebra ability.
Hurst, Michelle; Cordes, Sara
2017-02-27
Recent research suggests that fraction understanding is predictive of algebra ability; however, the relative contributions of various aspects of rational number knowledge are unclear. Furthermore, whether this relationship is notation-dependent or rather relies upon a general understanding of rational numbers (independent of notation) is an open question. In this study, college students completed a rational number magnitude task, procedural arithmetic tasks in fraction and decimal notation, and an algebra assessment. Using these tasks, we measured three different aspects of rational number ability in both fraction and decimal notation: (1) acuity of underlying magnitude representations, (2) fluency with which symbols are mapped to the underlying magnitudes, and (3) fluency with arithmetic procedures. Analyses reveal that when looking at the measures of magnitude understanding, the relationship between adults' rational number magnitude performance and algebra ability is dependent upon notation. However, once performance on arithmetic measures is included in the relationship, individual measures of magnitude understanding are no longer unique predictors of algebra performance. Furthermore, when including all measures simultaneously, results revealed that arithmetic fluency in both fraction and decimal notation each uniquely predicted algebra ability. Findings are the first to demonstrate a relationship between rational number understanding and algebra ability in adults while providing a clearer picture of the nature of this relationship. © 2017 The British Psychological Society.
Yantz. Jennifer
2013-01-01
The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting students' postsecondary success as STEM majors. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. In the present study, the connections…
Some fixed point results for rational type and subrational type contractive mappings
Huang Huaping
2017-08-01
Full Text Available In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97. Moreover, we give an example to support our results.
Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Ordered b-Metric Spaces
Farzaneh Zabihi
2014-01-01
Full Text Available We introduce the new notion of a hybrid rational Geraghty contractive mapping and investigate the existence of fixed point and coincidence point for such mappings in ordered b-metric spaces. We also provide an example to illustrate the results presented herein. Finally, we establish an existence theorem for a solution of an integral equation.
Are motorways rational from slime mould's point of view?
Adamatzky, Andrew; Alonso-Sanz, Ramon; van Dessel, Wesley; Ibrahim, Zuwairie; Ilachinski, Andrew; Jones, Jeff; Kayem, Anne V D M; Martinez, Genaro J; de Oliveira, Pedro; Prokopenko, Mikhail; Schubert, Theresa; Sloot, Peter; Strano, Emanuele; Yang, Xin-She
2012-01-01
We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, The Netherlands, UK, USA. For each geographical entity we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randic index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and ...
On the number of singular points of plane curves
Orevkov, S Y
1995-01-01
This is an extended, renovated and updated report on a joint work which the second named author presented at the Conference on Algebraic Geometry held at Saitama University, 15-17 of March, 1995. The main result is an inequality for the numerical type of singularities of a plane curve, which involves the degree of the curve, the multiplicities and the Milnor numbers of its singular points. It is a corollary of the logarithmic Bogomolov-Miyaoka-Yau's type inequality due to Miyaoka. It was first proven by F. Sakai at 1990 and rediscovered by the authors independently in the particular case of an irreducible cuspidal curve at 1992. Our proof is based on the localization, the local Zariski--Fujita decomposition and uses a graph discriminant calculus. The key point is a local analog of the BMY-inequality for a plane curve germ. As a corollary, a boundedness criterium for a family of plane curves has been obtained. Another application of our methods is the following fact: a rigid rational cuspidal plane curve canno...
Arithmetic Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Yin, Chen-Yang; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, kn...
McMullen, Jake; Hannula-Sormunen, Minna M.; Laakkonen, Eero; Lehtinen, Erno
2016-01-01
Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students' spontaneous focusing on…
Obersteiner, Andreas; Hoof, Jo Van; Verschaffel, Lieven; Dooren, Wim Van
2016-08-01
Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.
Multi-point quasi-rational approximants for the modified Bessel function I1(x)
Martin, P.; Olivares, J.; Cortés-Vega, L.; Sotomayor, A.
2016-08-01
Approximants for the modified Bessel function I1(x) has been found using the multi-point quasi-rational technique. The approximations here determined has good accuracy for any positive value of the variable, and it seems to be adequate for most of the works where this function are used. Furthermore, the approximants are simple to calculate numerically in a direct way or using any usual MAPLE or MATLAB software.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2015-05-01
To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.
Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction
Poom Kumam
2013-01-01
Full Text Available Ran and Reurings (2004 established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.
SPEED UP RATIONAL POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES BY FROBENIUS EQUATIONS
You Lin; Zhao Junzhong; Xu Maozhi
2006-01-01
Let q be a power of a prime and φ be the Frobenius endomorphism on E(Fqk), then q = tφ- φ2.Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that qs can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis (NB) or Optimal Normal Basis (ONB) is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about rithm. In addition, an effective algorithm is provided for finding such integer s.
The turning point in the number of traffic fatalities
Brüde, Ulf; Elvik, Rune
2015-01-01
The number of traffic fatalities reached a peak in many highly motorised countries around 1970. Some previous studies have suggested that the turning point in the number of traffic fatalities was inevitable and did not reflect a change in the underlying trends influencing the number of traffic...... fatalities. Other studies suggest that trends in traffic growth and fatality rate changed from before to after the turning point. This paper proposes two hypotheses about the turning point in the number of traffic fatalities. One hypothesis is that the long-term trends in traffic growth and fatality rate...... were the same before and after the turning point. The other hypothesis is that the long-term trends in traffic growth and fatality rate were different before and after the turning point was reached, in particular that the annual percentage decline in fatality rate became greater after the turning point...
Consistency of Trend Break Point Estimator with Underspecified Break Number
Jingjing Yang
2017-01-01
Full Text Available This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such as allowing a time trend in the model. Despite the consistency of break point estimators of level shifts, there are few papers on the consistency of trend shift break point estimators in the presence of an underspecified break number. The simulation study and asymptotic analysis in this paper show that the trend shift break point estimator does not converge to the true break points when the break number is underspecified. In the case of two trend shifts, the inconsistency problem worsens if the magnitudes of the breaks are similar and the breaks are either both positive or both negative. The limiting distribution for the trend break point estimator is developed and closely approximates the finite sample performance.
Geil, Hans Olav; Matsumoto, Ryutaroh
2009-01-01
We present a new bound on the number of Fq -rational places in an algebraic function field. It uses information about the generators of the Weierstrass semigroup related to a rational place. As we demonstrate, the bound has implications to the theory of towers of function fields....
Hunhold, Laslo
2017-01-01
This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are inadequate. In the course of this examination, this thesis builds theoretical foundations for IEEE 754 floating-point numbers, interval arithmetic based on the projectively extended real numbers and Unums.
Collective aspects of pre-service lower secondary teachers' knowledge on density of rational numbers
Putra, Zetra Hainul
2016-01-01
This study is about the design of hypothetical teacher tasks (HTTs) on density of rational numbers, developed based on the anthropological theory of the didactic (ATD), and used to investigate pre-service lower secondary teachers (PLSTs)’ mathematical and didactical knowledge. The PLSTs’ knowledge...... considered in this paper concerns mathematical and didactical techniques to solve the specific tasks on the HTTs. The collective aspects, mutual engagement, joint enterprise, and shared repertoire, are considered during their discussion. The findings show that there is a link between mathematical...
Blackett, S.A. [Univ. of Auckland (New Zealand). Dept of Engineering Science
1996-02-01
Numerical analysis is an important part of Engineering. Frequently relationships are not adequately understood, or too complicated to be represented by theoretical formulae. Instead, empirical approximations based on observed relationships can be used for simple fast and accurate evaluations. Historically, storage of data has been a large constraint on approximately methods. So the challenge is to find a sufficiently accurate representation of data which is valid over as large a range as possible while requiring the storage of only a few numerical values. Polynomials, popular as approximation functions because of their simplicity, can be used to represent simple data. Equation 1.1 shows a simple 3rd order polynomial approximation. However, just increasing the order and number of terms included in a polynomial approximation does not improve the overall result. Although the function may fit exactly to observed data, between these points it is likely that the approximation is increasingly less smooth and probably inadequate. An alternative to adding further terms to the approximation is to make the approximation rational. Equation 1.2 shows a rational polynomial, 3rd order in the numerator and denominator. A rational polynomial approximation allows poles and this can greatly enhance an approximation. In Sections 2 and 3 two different methods for fitting rational polynomials to a given data set are detailed. In Section 4, consideration is given to different rational polynomials used on adjacent regions. Section 5 shows the performance of the rational polynomial algorithms. Conclusions are presented in Section 6.
Applying inversion to construct planar, rational spirals that satisfy two-point G(2) Hermite data
Kurnosenko, A
2010-01-01
A method of two-point G(2) Hermite interpolation with spirals is proposed. To construct a sought for curve, the inversion is applied to an arc of some other spiral. To illustrate the method, inversions of parabola are considered in detail. The resulting curve is 4th degree rational. The method allows the matching of a wide range of boundary conditions, including those which require an inflection. Although not all G(2) Hermite data can be matched with a spiral generated from a parabolic arc, introducing one intermediate G(2) data solves the problem. Expanding the method by involving other spirals arcs is also discussed. (C) 2009 Elsevier B.V. All rights reserved.
ALGORITHM FOR SPHERICITY ERROR AND THE NUMBER OF MEASURED POINTS
HE Gaiyun; WANG Taiyong; ZHAO Jian; YU Baoqin; LI Guoqin
2006-01-01
The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine (CMM). The consummate criterion for the minimum zone of spherical surface is analyzed first, and then an approximation technique searching for the minimum sphericity error from the form data is studied. In order to obtain the minimum zone of spherical surface, the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps. Therefore the algorithm is precise and efficient. After the appropriate mathematical model for the approximation technique is created, a data processing program is developed accordingly. By processing the metrical data with the developed program, the spherical errors are evaluated when different numbers of measured points are taken from the same sample, and then the corresponding scatter diagram and fit curve for the sample are graphically represented. The optimal number of measured points is determined through regression analysis. Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective. On average, the obtained sphericity error is 5.78 μm smaller than the least square solution,whose accuracy is increased by 8.63%; The obtained optimal number of measured points is half of the number usually measured.
Vass, M; Hendriksen, C
2005-01-01
people and to consider different approaches when evaluating evidence of risk and benefit for the individual. Old people are facing a considerable risk of adverse drug reactions and recent initiatives, including the Continuous Medical Educational Efforts Programme, address issues of inappropriate...... state that a number of pharmacological regimens for older people are outperformed by non-pharmacological treatment alternatives involving competent individualised counselling and public provision of easy (transportation) possibilities for joining centres offering staff and equipment for physical......This paper discusses GP perspectives on the principles underlying rational pharmacotherapy for older people. The rising use of prescription medicine forces the GP to balance the benefit of evidence group-based appropriate drug use against the problems arising when medication is given to older...
Shifting of wrapped phase maps in the frequency domain using a rational number
Gdeisat, Munther A.; Burton, David R.; Lilley, Francis; Arevalillo-Herráez, Miguel; Abushakra, Ahmad; Qaddoura, Maen
2016-10-01
The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed both by using an initial computer simulation and is subsequently validated experimentally on real fringe patterns. The technique may offer in some cases the prospects of removing the necessity for a phase unwrapping process altogether and/or speeding up the phase unwrapping process. This may be beneficial in terms of potential increases in signal recovery robustness and also for use in time-critical applications.
Fixed Points on the Real numbers without the Equality Test
Korovina, Margarita
2002-01-01
In this paper we present a study of definability properties of fixed points of effective operators on the real numbers without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive...
A Software Library for Reliable Online-Arithmetic with Rational Numbers
Miguel Casado, Gregorio de; García Chamizo, Juan Manuel
2008-01-01
An overview of a novel calculation framework for scientific computing in integrable spaces is introduced. This paper discusses some implementation issues adopted for a software library devoted to exact rational online-arithmetic operators for periodic rational operands codified in fractional positional notation.
Yi-hua Zhong
2013-01-01
Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.
Sumit Chandok
2013-03-01
Full Text Available The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed $g$-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.
Height bound and preperiodic points for jointly regular families of rational maps
Lee, ChongGyu
2010-01-01
Silverman proved a height inequality for jointly regular family of rational maps and the author improved it for jointly regular pairs. In this paper, we provide the same improvement for jointly regular family; if S is a jointly regular set of rational maps, then \\sum_{f\\in S} \\dfrac{1}{\\deg f} h\\bigl(f(P) \\bigr) > (1+ \\dfrac{1}{r}) f(P) - C where r = \\max_{f\\in S} r(f).
Growth of the number of periodic points for meromorphic maps
2016-01-01
We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at most exponentially fast with respect to n and the exponential rate is at most equal to the algebraic entropy of f. Further estimates are given when X is a surface. Among the techniques introduced in this paper, the h-dimension of the density between two arbit...
Floating-Point Numbers with Error Estimates (revised)
Masotti, Glauco
2012-01-01
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a hardwired processor incorporat...
有限理性与KKM点集的稳定性%Bounded Rationality and Stability of KKM's Points Sets
张德金
2011-01-01
It has been studied actively in recent years the consider the bounded rationality in the study of the stability about the solution of nonlinear problems, whose results will fit with the practical situation more easily. In this paper, the unified conclusions of stability for nonlinear problems are given first, and then, with the use of applications of the unified model, problems' metric for KKM's points problems are constricted and rationality function for KKM’s points problems are defined, to discuss the stability of solutions for KKM's points problems on the bounded rationality. It is proved that KKM's points problems are satisfied all of hypothesis conditions of the unified conclusions, we receive the conclusions of structurally stable and robust. Then, it is proved that most of KKM's points problems( in the sense of Baire category) are structurally stable and robust to ε- equilibria, finally, the stability results on KKM's points problems are given. Moreover, We assume that people only have bounded rationality in the study, so we can enlarge the application scope of the results of the KKM's points problems.%文章首先给出有限理性非线性问题的稳定性结果,然后应用统一结果对KKM点问题构造了问题空间,定义了理性函数,讨论了有限理性下KKM点问题解的稳定性.通过证明其满足统一结论的假设条件,得到了有限理性下KKM点集结构稳定性和鲁棒性结论.并证明了大多数的KKM点问题在Baire分类意义上都是结构稳定的,对ε-平衡也都是鲁棒的,得到了有限理性下KKM点集稳定性的一系列结果.并且,由于在问题研究中考虑了人们只具有有限理性的假设条件,故扩展了KKM点问题结论的应用范围.
Quesne, C.
2016-10-01
The quantum oscillator and Kepler-Coulomb problems in d-dimensional spaces with constant curvature are analyzed from several viewpoints. In a deformed supersymmetric framework, the corresponding nonlinear potentials are shown to exhibit a deformed shape invariance property. By using the point canonical transformation method, the two deformed Schrödinger equations are mapped onto conventional ones corresponding to some shape-invariant potentials, whose rational extensions are well known. The inverse point canonical transformations then provide some rational extensions of the oscillator and Kepler-Coulomb potentials in curved space. The oscillator on the sphere and the Kepler-Coulomb potential in a hyperbolic space are studied in detail and their extensions are proved to be consistent with already known ones in Euclidean space. The partnership between nonextended and extended potentials is interpreted in a deformed supersymmetric framework. Those extended potentials that are isospectral to some nonextended ones are shown to display deformed shape invariance, which in the Kepler-Coulomb case is enlarged by also translating the degree of the polynomial arising in the rational part denominator.
S. V. Gautier
2013-01-01
Full Text Available Aim: to calculate number of the centers of transplantation according to real requirement of the population and a donor resource, to prove their geography and the nomenclature, providing with donor organs. Methods and results. The analysis and comparison of statistical data on population, number of the centers of transplantation, their transplant activity in Russia and abroad are made. Calculation of number of the centers of transplantation is carried out and justification of their geography is offered. The analysis of statistical data on hospitals in the Russia is made, calculation of a rational number of donor hospitals according to need for a donor resource is carried out. Justification of transplant coordination in territorial subjects of the Russia, in federal districts is offered. Justification of the nomenclature of the centers of transplantation and donor hospitals is offered.Conclusion. Settlement data on a rational number of the centers of transplantation, their geography and the nomenclature, providing with the donor organs, suitable developments for planning of the hi-tech medical care in territorial subjects of the Russia are obtained.
Verification of Numerical Programs: From Real Numbers to Floating Point Numbers
Goodloe, Alwyn E.; Munoz, Cesar; Kirchner, Florent; Correnson, Loiec
2013-01-01
Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.
Guo, Ying-jun; Wen, Zhi-Xiong; Zhang, Jie-Meng
2016-01-01
Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of Fibonacci sequence.
Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves
Aspinwall, Paul S; Aspinwall, Paul S.; Morrison, David R.
1998-01-01
We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.
DeWolf, M; Bassok, M; Holyoak, KJ
2015-01-01
© 2015 Elsevier Inc. To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuri...
Sense and Reference in the Design of Interactive Illustrations for Rational Numbers.
Ohlsson, Stellan
It is a common tactic in the teaching of arithmetic to provide the learner with pictures and embodiments of various kinds. However, the pedagogy of illustrations is not well understood. Analysis of the concept of meaning in relation to arithmetic shows that full understanding of arithmetic implies intellectual possession of a number of different…
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
Beelen, Peter; Ruano, Diego
2013-01-01
In this article we use techniques from coding theory to derive upper bounds for the number of rational places of the function field of an algebraic curve defined over a finite field. The used techniques yield upper bounds if the (generalized) Weierstrass semigroup (J Pure Appl Algebra 207(2), 243...
1988-05-03
allowed. If Wies are created or opened using such instan- tiations, the Use-..Error exception is raised. s Count type: The Count type for package Texto ...interactive input/output windows provided by the Rational Editor . When a job is run from package Program, options allow the user to specify what Standard
Rosane Ratzlaff da Rosa
2008-12-01
Full Text Available This article reports on an investigation which sought to determine if the use of spreadsheets in the teaching of rational numbers in elementary education contributes to learning and improved learning retention. The study was carried out with a sample of students from two sixth-grade classes in a public school in Porto Alegre. Results indicated that the use of spreadsheets favored learning and made the classes more participatory for the students, who were able to visualize the processes they were working with. A second test applied five months after the first test showed that students who used the spreadsheets had greater learning retention of the contents. The results also show that the students felt comfortable with the technology, and almost all reported that they were more motivated by the use of computers in the classroom, despite less-than-ideal laboratory conditions. Key-words: Rational Numbers. Teaching with Spreadsheet. Teaching Rational Numbers using Spreadsheet.Este artigo relata uma investigação que procurou determinar se o uso de planilha como recurso no ensino dos números racionais na Educação Básica contribui para a aprendizagem e uma maior retenção dessa aprendizagem a médio prazo. A investigação foi realizada com uma amostra de alunos de duas turmas da sexta série de uma escola pública de Porto Alegre. Os resultados indicaram que o uso da planilha favorece a aprendizagem e torna as aulas mais participativas para os alunos, que conseguiram visualizar os processos com os quais trabalharam. Um segundo teste aplicado cinco meses após o primeiro mostrou que os alunos que utilizaram a planilha apresentaram uma maior retenção do conteúdo. Os resultados apontam ainda que os alunos se sentem à vontade com a tecnologia e quase todos disseram ficarem mais motivados com as aulas utilizando o computador apesar das condições do laboratório utilizado não ser a ideal. Palavras-chave: Números Racionais. Ensino com a
The GenePOC Platform, a Rational Solution for Extreme Point-of-Care Testing
Luc Bissonnette
2016-05-01
Full Text Available Extreme point-of-care (POC testing for infections, as performed (endured in low-resource settings, developing countries, tropical areas, or in conditions following emergency crises or natural disasters, must be undertaken under environmental, logistic, and societal conditions which impose a significant deal of stress on local human populations and healthcare providers. For disease diagnostics or management, simple and robust biomedical equipment and reagents are required and needed. This chapter aims to overview some of these stresses (requirements and intends to describe some of the solutions already engineered at the heart of centripetal (centrifugal microfluidic platforms such as that of GenePOC Inc. to enable rapid, robust, and reproducible nucleic acid-based diagnostics of infectious diseases, to better control the morbidity and mortality of infections and the expanding threat posed by antimicrobial resistance.
Number needed to treat: solid science or a path to pernicious rationing?
Black, H R; Crocitto, M T
1998-08-01
Basing clinical practice decisions on currently available evidence from clinical trials may result in suboptimal care in the real-world practice of medicine. The problem stems from both the quality of data and the means by which the data have been interpreted. In an attempt to remedy the situation, a term based on an assessment of all risk factors and comorbidity has been suggested and made more easily translatable to clinical decision making. This term, the reciprocal of absolute risk reduction, is the number needed to treat (NNT), an idea that has gained wide acceptance. There are, however, risks that the simplicity of the NNT will be misused to guide reimbursement decisions and potentially prevent patients from receiving optimal care. This seemingly objective measure may be seriously flawed if the data on which this measure is based do not necessarily reflect the results that real world doctors achieve in practice. These problems could lead to the misguided allocation of health care resources. It is therefore incumbent upon us to closely evaluate the data on which NNTs are based and, if necessary, to arrive at more accurate NNTs. In our view, such data should be gleaned from effectiveness trials done by real world doctors in real world settings with real world volunteers. Large simple trials, as have already been performed in a number of therapeutic areas, especially for acute management of myocardial infarction and in acquired immune deficiency syndrome, offer the best likelihood of yielding this crucial information. We need to be sure that future trials of chronic conditions such as hypertension are done with this trial paradigm, so that those who pay for care have the accurate knowledge needed to spend their money wisely.
Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong
2015-07-01
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
Shao, Chenxi, E-mail: cxshao@ustc.edu.cn; Xue, Yong; Fang, Fang; Bai, Fangzhou [Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Yin, Peifeng [Department of Computer Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16801 (United States); Wang, Binghong [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2015-07-15
The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
Beelen, Peter; Ruano, Diego
2011-01-01
In [5] an upper bound for the number of points on an al- gebraic curve dened over a nite eld was derived. In this article we generalize their result by considering Weierstrass groups of several points simultaneously....
Bounded Rationality and Fixed Point Problem Well-Possedness%考虑有限理性的良定不动点问题研究
刘益波; 高维
2011-01-01
本文引入了新的不动点问题良定的定义,应用有限理性模型M研究了良定不动点问题,给出了不动点问题良定的充分条件.%This paper introduces a new definition of the fixed point problem well-posedness, applying the finite rational model set M to study well-posedness of the fixed point problem, sufficient conditions of the fixed point problem ′s well-pesedness are given.
On the Required Number of Antennas in a Point-to-Point Large-but-Finite MIMO System
Makki, Behrooz
2015-11-12
In this paper, we investigate the performance of the point-to-point multiple-input-multiple-output (MIMO) systems in the presence of a large but finite numbers of antennas at the transmitters and/or receivers. Considering the cases with and without hybrid automatic repeat request (HARQ) feedback, we determine the minimum numbers of the transmit/receive antennas which are required to satisfy different outage probability constraints. We study the effect of the spatial correlation between the antennas on the system performance. Also, the required number of antennas are obtained for different fading conditions. Our results show that different outage requirements can be satisfied with relatively few transmit/receive antennas. © 2015 IEEE.
Houde Han; Zhongyi Huang
2008-01-01
In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L2-norm.
Cook Inlet and Kenai Peninsula, Alaska ESI: ROAD_MRK (Road Number Points)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector points used in plotting the road numbers on the summary maps. It comprises a portion of the Environmental Sensitivity Index (ESI) data...
STUDENTS? LEARNING DIFFICULTIES AND MISCONCEPTIONS IN POINTING THE FRACTIONS ON THE NUMBER LINE
Cahit PESEN
2008-01-01
This study has been carried out to determine the 3rd grade students? n=113 learning difficulties in pointing the fractions on number line and to find out the misconceptions lying behind common mistakes For this purpose we have tried to determine learning difficulties in matching fractions with points on the number line and misconceptions by using the ?Diagnosis test? method on the 3rd grade students n=113 In this matching the learning difficulties and misconceptions these students enc...
Students’ learning difficulties and misconceptions in pointing the fractions on the number line
Cahit PESEN
2008-01-01
This study has been carried out to determine the 3rd grade students’ (n=113) learning difficulties in pointing the fractions on number line and to find out the misconceptions lying behind common mistakes. For this purpose, we have tried to determine learning difficulties in matching fractions with points on the number line and misconceptions by using the “Diagnosis test” method on the 3rd grade students (n=113). In this matching, the learning difficulties and misconceptions these students enc...
Intersection numbers on the relative Hilbert schemes of points on surfaces
Gholampour, Amin; Sheshmani, Artan
2015-01-01
We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the non-relative Hilbert schemes. In particular, we obtain a relative...
ON THE HEILBRONN NUMBER OF n-NONCOLINEAR POINTS IN THE PLANE
YuJian
1996-01-01
In this article,we have given the definition of the Heilbronn number of nnoncollinear points in the plane. By this, we got the exact value of Hs which is the exact upper bound of Hs (K), where Hs (K) is any Heilbronn number in common sense.
Zoev, I. V.; Beresnev, A. P.; Mytsko, E. A.; Malchukov, A. N.
2017-02-01
An important aspect of modern automation is machine learning. Specifically, neural networks are used for environment analysis and decision making based on available data. This article covers the most frequently performed operations on floating-point numbers in artificial neural networks. Also, a selection of the optimum value of the bit to 14-bit floating-point numbers for implementation on FPGAs was submitted based on the modern architecture of integrated circuits. The description of the floating-point multiplication (multiplier) algorithm was presented. In addition, features of the addition (adder) and subtraction (subtractor) operations were described in the article. Furthermore, operations for such variety of neural networks as a convolution network - mathematical comparison of a floating point (‘less than’ and ‘greater than or equal’) were presented. In conclusion, the comparison with calculating units of Atlera was made.
Computer Arithmetic Algorithms for Mega-Digit Floating Point Numbers' Precision
Musbah J. Aqel
2007-01-01
Full Text Available IEEE standard 754 floating point is the most common representation used for floating point numbers, and many computer arithmetic algorithms are developed for basic operations on this standard. In this study, new computer algorithms are proposed to increase the precision range and to solve some problems that are available while using these algorithms. However, these algorithms provide an optional range of required accuracy (Mega-Digit precision to meet new computer's applications.
The fluctuations in the number of points of smooth plane curves over finite fields
Bucur, Alina; Feigon, Brooke; Lalín, Matilde
2009-01-01
In this note, we study the fluctuations in the number of points of smooth projective plane curves over finite fields $\\mathbb{F}_q$ as $q$ is fixed and the genus varies. More precisely, we show that these fluctuations are predicted by a natural probabilistic model, in which the points of the projective plane impose independent conditions on the curve. The main tool we use is a geometric sieving process introduced by Poonen.
Students’ learning difficulties and misconceptions in pointing the fractions on the number line
Cahit PESEN
2008-06-01
Full Text Available This study has been carried out to determine the 3rd grade students’ (n=113 learning difficulties in pointing the fractions on number line and to find out the misconceptions lying behind common mistakes. For this purpose, we have tried to determine learning difficulties in matching fractions with points on the number line and misconceptions by using the “Diagnosis test” method on the 3rd grade students (n=113. In this matching, the learning difficulties and misconceptions these students encounter have been determined and some proposals have been developed to come over these difficulties.
The Tipping Point: F-Score as a Function of the Number of Retrieved Items
Guns, Raf; Lioma, Christina; Larsen, Birger
2012-01-01
One of the best known measures of information retrieval (IR) performance is the F-score, the harmonic mean of precision and recall. In this article we show that the curve of the F-score as a function of the number of retrieved items is always of the same shape: a fast concave increase to a maximum......, followed by a slow decrease. In other words, there exists a single maximum, referred to as the tipping point, where the retrieval situation is 'ideal' in terms of the F-score. The tipping point thus indicates the optimal number of items to be retrieved, with more or less items resulting in a lower F...
EXPECTED NUMBER OF ITERATIONS OF INTERIOR-POINT ALGORITHMS FOR LINEAR PROGRAMMING
Si-ming Huang
2005-01-01
We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the expected and anticipated number of iterations of these algorithms is bounded above by O(n1,5). The random LP problem is Todd's probabilistic model with the Cauchy distribution.
On the optimal number of scale points in graded paired comparisons
Beuckelaer, A. De; Toonen, S.; Davidov, E.
2013-01-01
In market research, it is common practice to measure individuals’ brand or product preference through graded paired comparisons (GPCs). One important decision concerns the (odd) number of scale points (e.g., five, seven, nine, or eleven) that has to be assigned to either brands or products in each
Comparing Number Lines and Touch Points to Teach Addition Facts to Students with Autism
Cihak, David F.; Foust, Jennifer L.
2008-01-01
Three elementary students with autism were taught single-digit addition problem-solving skills using number and touch-point strategies. Prior to the study, all students were unable to correctly calculate single-digit addition problems. An alternating-treatments design was used to compare the acquisition performance of single-digit addition…
Average number of iterations of some polynomial interior-point--Algorithms for linear programming
无
2000-01-01
We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite termination technique, is bounded above by O(n1.5). The random LP problem is Todd's probabilistic model with the standard Gauss distribution.
Intervention measures, turning point, and reproduction number for dengue, Singapore, 2005.
Hsieh, Ying-Hen; Ma, Stefan
2009-01-01
The 2005 dengue outbreak in Singapore cumulated in > 14,000 cases and 27 reported dengue deaths. We fit the single-phase Richards model to weekly dengue notification numbers to detect the turning point for the outbreak, which enables us to study the impact of intervention measures relating to the turning point. The results indicate that turning point had most likely occurred in late August or early September, before large-scale intervention measures were implemented. The "initial" reproduction number for the outbreak is estimated to be ~1.89-2.23 (95% confidence interval: 1.15-3.00). One of the lessons learned from the 2003 severe acute respiratory syndrome (SARS) outbreak is that multiple phases of outbreak were observed in some affected countries when efforts to intensify intervention or to sustain vigilance were compromised. Intensive and continuing efforts in the implementation of control measures are essential in reducing further dengue occurrences during any resurgence of dengue.
Reznik, A. L.; Tuzikov, A. V.; Solov'ev, A. A.; Torgov, A. V.
2016-11-01
Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.
On the precision attainable with various floating-point number systems
Brent, Richard P
2010-01-01
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the same range and requiring the same word length. In particular, we compare different choices of base (or radix) in the usual floating-point systems. The emphasis is on the choice of F, not on the details of the number representation or the arithmetic, but both rounded and truncated arithmetic are considered. Theoretical results are given, and some simulations of typical floating-point computations (forming sums, solving systems of linear equations, finding eigenvalues) are described. If the leading fraction bit of a normalized base 2 number is not stored explicitly (saving a bit), and the criterion is to minimize the mean square roundoff error, then base 2 is best. If unnormalized numbers are allowed, so the first bit must be stored explicitly, then base 4 (or sometimes base...
The Factorization of xn+1 on the Rational Number Field%xn＋1在有理数域上的因式分解
陈运栋; 谷秀川
2014-01-01
Factorization of f(x)=xn+1 in rational field Q[x ]leads to the following conclusions.For any positive integer n ,let H(n )denote the number of odd divisors d of n with d>1 .In this paper,using the knowledge of elementary number theory and modern algebraic,we prove that the polynomial xn+1 is bound to resolve into a product of H(n )+1 irreducible factors on the rational number field ,that is D(f )= H(n )+1 .%从特殊情况研究多项式f（x）＝xn＋1在有理数域上的因式分解．对于正整数，设 H （n）是n的大于1的奇约数的个数．本文用初等数论和近世代数的知识证明了：多项式xn＋1在有理数域上可分解为 H （n）＋1个不可约因式的乘积，即D（f）＝ H（n）＋1．
A comparison of floating point and logarithmic number systems for FPGAs.
Hauck, Scott (University of Washington, Seattle, WA); Wood, Aaron (University of Washington, Seattle, WA); Beauchamp, Michael (University of Washington, Seattle, WA); Haselman, Michael (University of Washington, Seattle, WA); Hemmert, K. Scott; Underwood, Keith Douglas
2005-02-01
There have been many papers proposing the use of logarithmic numbers (LNS) as an alternative to floating point because of simpler multiplication, division and exponentiation computations. However, this advantage comes at the cost of complicated, inexact addition and subtraction, as well as the need to convert between the formats. In this work, we created a parameterized LNS library of computational units and compared them to an existing floating point library. Specifically, we considered multiplication, division, addition, subtraction, and format conversion to determine when one format should be used over the other and when it is advantageous to change formats during a calculation.
Oesch, Denis W; Sanchez, Darryl J; Matson, Charles L
2010-10-11
Optical waves propagating through atmospheric turbulence develop spatial and temporal variations in their phase. For sufficiently strong turbulence, these phase differences can lead to interference in the propagating wave and the formation of branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, we show that these branch points can be used to estimate the number and velocities of atmospheric layers. We describe how to carry out this estimation process and demonstrate its robustness in the presence of sensor noise.
Quantum mechanics in a space with a finite number of points
Arik, Metin; Ildes, Medine
2016-04-01
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the translation operator becomes nonunitary due to the end points. This uniquely defines an algebra that has the desired unique representation. Energy eigenvalues and energy wave functions for both cases are found. As expected, in the continuum limit the solution for the nonperiodic case becomes the same as the solution of an infinite one-dimensional square well and the periodic case solution becomes the same as the solution of a particle in a box with periodic boundary conditions.
Lourdes de la Rosa Onuchic
2008-12-01
Full Text Available We address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education.Neste artigo, pretende-se abordar as diferentes “personalidades” do número racional e o conceito de proporcionalidade, analisando as possibilidades de utilizar a Metodologia de Ensino-Aprendizagem de Matemática através da Resolução de Problemas. Essa metodologia parte do princípio de que a construção do conhecimento pode ser realizada a partir de problemas geradores de novos conceitos e novos conteúdos. Os diferentes significados do número racional: ponto racional, quociente, fração, razão e operador são construtos que dependem das teorias matemáticas em que se inserem e das situações a que se referem na resolução de problemas. Serão apresentados alguns dados que foram desenvolvidos em cursos de formação continuada
The analysis of the number of fixed points in the key extending algorithm of RC4
2008-01-01
The probabilities of the state transitions of the initial value So in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.
Rational Curves on Calabi-Yau Threefolds
Katz, S
1992-01-01
The point is to compare the mathematical meaning of the ``number of rational curves on a Calabi-Yau threefold'' to the meaning ascribed to the same notion by string theorists. By considering mirror symmetry applied to conformal field theories corresponding to strings propagating in quintic hypersurfaces in projective 4-space, Candelas, de la Ossa, Green and Parkes calculated the ``number of rational curves on the hypersurface'' by comparing three point functions. Actually, the number of curves may be infinite for special examples; what is really being calculated is a path integral. The point of this talk is to give mathematical techniques and examples for computing the finite number that ``should'' correspond to an infinite family of curves (which coincides with that given by the path integral in every known instance), and to suggest that these techniques should provide the answer to the not yet solved problem of how to calculate instanton corrections to the three point function in general.
The Number Of Magnetic Null Points In The Quiet Sun Corona
Longcope, D W
2008-01-01
The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points. These points can be found directly in a potential field extrapolation or their density can be estimated from Fourier spectrum of the magnetogram. The spectral estimate, which assumes that the extrapolated field is random, homogeneous and has Gaussian statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO's MDI. The majority of null points occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate for the modulation tran...
Approximation of quadrilaterals by rational quadrilaterals in the plane
2017-02-01
Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain diophantine equations. We look at a number of such questions including the question of approximating arbitrary triangles and quadrilaterals by those with rational sides, diagonals and areas. We transform these problems into questions on the existence of infinitely many rational solutions on a two parameter family of quartic curves. This is further transformed to a two parameter family of elliptic curves to deduce our main result concerning density of points on a line which are at a rational distance from three collinear points (Theorem 4). We deducefrom this a new proof of density of rational quadrilaterals in the space of all quadrilaterals (Theorem 39). The other main result (Theorem 3) of this article is on the density of rational triangles which is related to analyzing rational points on the unit circle. Interestingly, this enables us to deduce that parallelograms with rational sides and area are dense in the class of all parallelograms. We also give a criterion for density of certain sets in topological spaces using local product structure and prove the density Theorem 6 in the appendix section. An application of this proves the density of rational points as stated in Theorem 31.
Baugher, Benjamin
2008-01-01
We prove the main conjecture from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the metric dependence and asymptotic minimization of the expected number \\mathcal{N}^{crit}_{N,h} of critical points of random holomorphic sections of the Nth tensor power of a positive line bundle. The first non-topological term in the asymptotic expansion of \\mathcal{N}^{crit}_{N,h} is the the Calabi functional multiplied by the constant \\be_2(m) which depends only on the dimension of the manifold. We prove that \\be_2(m) is strictly positive in all dimensions, showing that the expansion is non-topological for all m, and that the Calabi extremal metric, when it exists, asymptotically minimizes \\mathcal{N}^{crit}_{N,h}.
On the distribution of the number of points on a family of curves over finite fields
Mak, Kit-Ho
2011-01-01
Let $p$ be a large prime, $\\ell\\geq 2$ be a positive integer, $m\\geq 2$ be an integer relatively prime to $\\ell$ and $P(x)\\in\\mathbb{F}_p[x]$ be a polynomial which is not a complete $\\ell'$-th power for any $\\ell'$ for which $GCD(\\ell',\\ell)=1$. Let $\\mathcal{C}$ be the curve defined by the equation $y^{\\ell}=P(x)$, and take the points on $\\mathcal{C}$ to lie in the rectangle $[0,p-1]^2$. In this paper, we study the distribution of the number of points on $\\mathcal{C}$ inside a small rectangle among residue classes modulo $m$ when we move the rectangle around in $[0,p-1]^2$.
Mayo, David J.
1998-01-01
The rational suicide paradigm is contrasted with the traditional view of the mental health professions. Historical background on suicide in western civilization is supplied and the concept of rationality elucidated. Parallels between the questions of refusing life-prolonging therapy and rational suicide are discussed, as are reasons for suicide.…
Stratlets: Low Reynolds Number Point-Force Solutions in a Stratified Fluid
Ardekani, A. M.; Stocker, R.
2010-08-01
We present fundamental solutions of low Reynolds number flows in a stratified fluid, including the case of a point force (Stokeslet) and a doublet. Stratification dramatically alters the flow by creating toroidal eddies, and velocity decays much faster than in a homogeneous fluid. The fundamental length scale is set by the competition of buoyancy, diffusion and viscosity, and is O(100μm-1mm) in aquatic environments. Stratification can therefore affect the swimming of small organisms and the sinking of marine snow particles, and diminish the effectiveness of mechanosensing in the ocean.
Viet-Thanh Pham
2016-01-01
Full Text Available Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.
FINITE VARIANCE OF THE NUMBER OF STATIONARY POINTS OF A GAUSSIAN RANDOM FIELD
Estrade, Anne; Fournier, Julie
2015-01-01
Let X be a real-valued stationary Gaussian random field defined on $R^d$ (d ≥ 1), with almost every realization of class $C^2$. This paper is concerned with the random variable giving the number of points in $T$ (a compact set of $R^d$) where the gradient $X'$ takes a fixed value $v\\in R^d$, $N_{X'}(T, v) = \\{t \\in T : X'(t) = v\\}$. More precisely, it deals with the finiteness of the variance of $N_{X'} (T, v)$, under some non-degeneracy hypothesis on $X$. For d = 1, the so-called " Geman con...
Bertola, Marco
2010-01-01
The semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials is studied in a full scaling neighborhood D of the point of gradient catastrophe (x_0,t_0). This neighborhood contains the region of modulated plane wave (with rapid phase oscillations), as well as the region of fast amplitude oscillations (spikes). In this paper we establish the following universal behaviors of the NLS solutions near the point of gradient catastrophe: i) each spike has the height 3|q_0(x_0,t_0,epsilon)| and uniform shape of the rational breather solution to the NLS, scaled to the size O(epsilon); ii) the location of the spikes are determined by the poles of the tritronquee solution of the Painleve I (P1) equation through an explicit diffeomorphism between D and a region into the Painleve plane; iii) if (x,t) belongs to D but lies away from the spikes, the asymptotics of the NLS solution q(x,t,epsilon) is given by the plane wave approximation q_0(x,t,epsilon...
Cholewa, Michał
2011-01-01
This paper presents a method of choosing number of states of a HMM based on number of critical points of the motion capture data. The choice of Hidden Markov Models(HMM) parameters is crucial for recognizer's performance as it is the first step of the training and cannot be corrected automatically within HMM. In this article we define predictor of number of states based on number of critical points of the sequence and test its effectiveness against sample data.
Computational Intelligence Determines Effective Rationality
无
2008-01-01
Rationality is a fundamental concept in economics. Most researchers will accept that human beings are not fully rational.Herbert Simon suggested that we are "bounded rational". However, it is very difficult to quantify "bounded rationality", and therefore it is difficult to pinpoint its impact to all those economic theories that depend on the assumption of full rationality. Ariel Rubinstein proposed to model bounded rationality by explicitly specifying the decision makers' decision-making procedures. This paper takes a computational point of view to Rubinstein's approach. From a computational point of view, decision procedures can be encoded in algorithms and heuristics. We argue that, everything else being equal, the effective rationality of an agent is determined by its computational power - we refer to this as the computational intelligence determines effective rationality (CIDER) theory. This is not an attempt to propose a unifying definition of bounded rationality. It is merely a proposal of a computational point of view of bounded rationality. This way of interpreting bounded rationality enables us to (computationally) reason about economic systems when the full rationality assumption is relaxed.
Minimum Number of Observation Points for LEO Satellite Orbit Estimation by OWL Network
Park, Maru; Jo, Jung Hyun; Cho, Sungki; Choi, Jin; Kim, Chun-Hwey; Park, Jang-Hyun; Yim, Hong-Suh; Choi, Young-Jun; Moon, Hong-Kyu; Bae, Young-Ho; Park, Sun-Youp; Kim, Ji-Hye; Roh, Dong-Goo; Jang, Hyun-Jung; Park, Young-Sik; Jeong, Min-Ji
2015-12-01
By using the Optical Wide-field Patrol (OWL) network developed by the Korea Astronomy and Space Science Institute (KASI) we generated the right ascension and declination angle data from optical observation of Low Earth Orbit (LEO) satellites. We performed an analysis to verify the optimum number of observations needed per arc for successful estimation of orbit. The currently functioning OWL observatories are located in Daejeon (South Korea), Songino (Mongolia), and Oukaïmeden (Morocco). The Daejeon Observatory is functioning as a test bed. In this study, the observed targets were Gravity Probe B, COSMOS 1455, COSMOS 1726, COSMOS 2428, SEASAT 1, ATV-5, and CryoSat-2 (all in LEO). These satellites were observed from the test bed and the Songino Observatory of the OWL network during 21 nights in 2014 and 2015. After we estimated the orbit from systematically selected sets of observation points (20, 50, 100, and 150) for each pass, we compared the difference between the orbit estimates for each case, and the Two Line Element set (TLE) from the Joint Space Operation Center (JSpOC). Then, we determined the average of the difference and selected the optimal observation points by comparing the average values.
Birla, Bhagyashree S; Chou, Hui-Hsien
2015-01-01
Gene synthesis is frequently used in modern molecular biology research either to create novel genes or to obtain natural genes when the synthesis approach is more flexible and reliable than cloning. DNA chemical synthesis has limits on both its length and yield, thus full-length genes have to be hierarchically constructed from synthesized DNA fragments. Gibson Assembly and its derivatives are the simplest methods to assemble multiple double-stranded DNA fragments. Currently, up to 12 dsDNA fragments can be assembled at once with Gibson Assembly according to its vendor. In practice, the number of dsDNA fragments that can be assembled in a single reaction are much lower. We have developed a rational design method for gene construction that allows high-number dsDNA fragments to be assembled into full-length genes in a single reaction. Using this new design method and a modified version of the Gibson Assembly protocol, we have assembled 3 different genes from up to 45 dsDNA fragments at once. Our design method uses the thermodynamic analysis software Picky that identifies all unique junctions in a gene where consecutive DNA fragments are specifically made to connect to each other. Our novel method is generally applicable to most gene sequences, and can improve both the efficiency and cost of gene assembly.
Bhagyashree S Birla
Full Text Available Gene synthesis is frequently used in modern molecular biology research either to create novel genes or to obtain natural genes when the synthesis approach is more flexible and reliable than cloning. DNA chemical synthesis has limits on both its length and yield, thus full-length genes have to be hierarchically constructed from synthesized DNA fragments. Gibson Assembly and its derivatives are the simplest methods to assemble multiple double-stranded DNA fragments. Currently, up to 12 dsDNA fragments can be assembled at once with Gibson Assembly according to its vendor. In practice, the number of dsDNA fragments that can be assembled in a single reaction are much lower. We have developed a rational design method for gene construction that allows high-number dsDNA fragments to be assembled into full-length genes in a single reaction. Using this new design method and a modified version of the Gibson Assembly protocol, we have assembled 3 different genes from up to 45 dsDNA fragments at once. Our design method uses the thermodynamic analysis software Picky that identifies all unique junctions in a gene where consecutive DNA fragments are specifically made to connect to each other. Our novel method is generally applicable to most gene sequences, and can improve both the efficiency and cost of gene assembly.
Birla, Bhagyashree S.; Chou, Hui-Hsien
2015-01-01
Gene synthesis is frequently used in modern molecular biology research either to create novel genes or to obtain natural genes when the synthesis approach is more flexible and reliable than cloning. DNA chemical synthesis has limits on both its length and yield, thus full-length genes have to be hierarchically constructed from synthesized DNA fragments. Gibson Assembly and its derivatives are the simplest methods to assemble multiple double-stranded DNA fragments. Currently, up to 12 dsDNA fragments can be assembled at once with Gibson Assembly according to its vendor. In practice, the number of dsDNA fragments that can be assembled in a single reaction are much lower. We have developed a rational design method for gene construction that allows high-number dsDNA fragments to be assembled into full-length genes in a single reaction. Using this new design method and a modified version of the Gibson Assembly protocol, we have assembled 3 different genes from up to 45 dsDNA fragments at once. Our design method uses the thermodynamic analysis software Picky that identifies all unique junctions in a gene where consecutive DNA fragments are specifically made to connect to each other. Our novel method is generally applicable to most gene sequences, and can improve both the efficiency and cost of gene assembly. PMID:26716828
Mamona-Downs, Joanna K.; Megalou, Foteini J.
2013-01-01
The aim of this paper is to examine students' understanding of the limiting behavior of a function from [set of real numbers][superscript 2] to [set of real numbers] at a point "P." This understanding depends on which definition is used for a limit. Several definitions are considered; two of these concern the notion of a neighborhood of "P", while…
A Note on the Existence of a Specified Number of Interior Points
WEI Xiang-lin; DING Ren
2012-01-01
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set.For any integer k ≥ 1,let h(k) be the smallest integer such that every set of points in the plane,no three collinear,with at least h(k) interior points,has a subset of points with exactly k or k + 1 interior points of P.We prove that h(5) =11.
Prediction uncertainty of plume characteristics derived from a small number of measuring points
French, H. K.; van der Zee, S. E. A. T. M.; Leijnse, A.
A small number of measuring points may inflict a bias on the characterisation of flow and transport based on field experiments in the unsaturated zone. Simulation of pure advective transport of a Gaussian plume through a setup of 30 regularly placed measuring points revealed regular temporal fluctuations about the real spatial moments. An irregular setup predicted both irregular fluctuations and larger discrepancies from the real value. From these considerations, a regular setup is recommended. Spatial moments were sensitive to the plume size relative to the distance between individual measuring points. To reduce prediction errors of the variance, the distance between the measuring points should be less than twice the standard deviation of the examined plume. The total size of the setup should cover several standard deviations of the plume to avoid mass being lost from the monitored area. Numerical simulations of a dispersing plume (comparing calculations based on 9000 nodes with 30 measuring points) revealed that vertical and horizontal centres of mass were predicted well at all degrees of heterogeneity, and the same was the case for horizontal variances. Vertical variances were more susceptible to prediction errors, but estimates were of the same order of magnitude as the real values. Résumé Lorsque l'on cherche à caractériser l'écoulement et le transport à partir d'expériences de terrain dans la zone saturée, il arrive qu'un petit nombre de points introduisent un biais. La simulation d'un transport purement advectif d'un panache gaussien au travers d'un ensemble de 30 points de mesures espacés régulièrement fait apparaître des variations temporelles régulières autour des moments spatiaux réels. Un ensemble irrégulier conduit à prédire à la fois des variations irrégulières et de plus grandes divergences par rapport à la valeur réelle. A partir de ces constations, un ensemble régulier est recommandé. Les moments spatiaux sont apparus
Hougaard, Jens Leth; Moreno-Ternero, Juan D.; Østerdal, Lars Peter Raahave
The standard problem of adjudicating conflicting claims describes a situation in which a given amount of a divisible good has to be allocated among agents who hold claims against it exceeding the available amount. This paper considers more general rationing problems in which, in addition to claims......, there exist baselines (to be interpreted as objective entitlements, ideal targets, or past consumption) that might play an important role in the allocation process. The model we present is able to accommodate real-life rationing situations, ranging from resource allocation in the public health care sector...... to international protocols for the reduction of greenhouse emissions, or water distribution in drought periods. We define a family of allocation methods for such general rationing problems - called baseline rationing rules - and provide an axiomatic characterization for it. Any baseline rationing rule within...
Positive circuits and maximal number of fixed points in discrete dynamical systems
Richard, Adrien
2008-01-01
The biologist Ren\\'e Thomas conjectured, twenty years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of multiple stable states. Recently, Richard and Comet stated and proved this conjecture for systems whose dynamics is described by the iterations of a map $F$ which operates on the product $X$ of $n$ finite intervals of integers. In this paper, we widely extend the result of Richard and Comet by exhibiting an upper bound on the number of fixed points for $F$ which only depends on $X$ and on the topology of the positive circuits of the interaction graph associated with $F$. Our motivation for this work comes from biology. The maps $F$ we focus on are indeed extensively used to described the behavior of gene regulatory networks, and when such a network is studied, the first reliable data often concern its interaction graph, so that the bound we establish can be used, in practice, to obtain valuable information about the numbe...
Identify Fractions and Decimals on a Number Line
Shaughnessy, Meghan M.
2011-01-01
Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…
Breyer, Nike Ulrike
2011-01-01
The nineteenth century "movement for rational clothing" not only aimed at reforming women's clothes (leaving behind corset-fashion), it set out to improve women's rights in general. Few people know that footwear also was modernized in the second half of the nineteenth century. After shoes had been made for 350 years on the basis of a symmetry pattern, without or with almost invisible distinction between left and right feet, scientists around the Frankfurt born professor of anatomy Georg Hermann von Meyer (1815-1892) demanded with him radical reform of footwear--for both sexes--using new lasts that were modelled on the natural shape of feet. Around the turn of the century, after physicians, shoemakers and hygienists had spent decades debating new ideas, members of the Wandervogel movement adopted the issue for their own purposes and chose anatomic over fashionable yet unhealthy fits which tended to be pointed, slim and--above all--symmetrical. Once the Wandervogel movement had split into several smaller groupings in 1904 and become part of the Jugendbewegung (youth movement), some of its members wanted clothing to also carry symbolic meaning. Naturally-shaped hygienic boots should no longer just allow for walking without damage to the feet: they should become the embodiment of a new spirit and, beyond that, of a reformed society. A new "lay practice" and "do-it-yourself"-shoemaking replaced former academic programs for new natural footwear. Interestingly enough, alongside those quite radical concepts, a kind of "footwear reform light" established itself in the market: on the surface only slightly different from the old-fashioned, symmetrical shoes, these "modern" pairs, which consisted of a right and left shoe, remained successful even after the world wars and became the new standard in the twentieth century, because the shoes made according to this pattern lasted longer, fitted better and were more comfortable.
ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS
SUN Jingxian; ZHANG Kemei
2003-01-01
In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.
Abu Bakar, Ahmad Syafadhli Bin
2015-01-01
The concept of ranking fuzzy numbers has received significant attention from the research community due to its successful applications for decision making. It complements the decision maker exercise their subjective judgments under situations that are vague, imprecise, ambiguous and uncertain in nature. The literature on ranking fuzzy numbers show that numerous ranking methods for fuzzy numbers are established where all of them aim to correctly rank all sets of fuzzy numbers that mimic real d...
Degree of a isolated real point or a singular complex point on a plane curve defined over Q
Hansen, Johan Peder
2010-01-01
Let $X$ be a curve in the affine plane defined by a reduced polynomial of degree $d$ with rational coefficients. Assume that $P$ is an isolated real point or a singular complex point on the curve $X$. The coordinates of $P$ are algebraic numbers over the rationals of degree at most $d^2$. The res...
Harmening, Corinna; Neuner, Hans
2016-09-01
Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.
Spectral Properties of the Two-Dimensional Laplacian with a Finite Number of Point Interactions
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1997-01-01
We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a symmetric (Hermitian) operator in functional analysis. The eigenvalues of this system are obtained as the poles of a transition matrix which has size $N$. Closely examining a generic behavior of the eigenvalues of the transition matrix as a function of the energy, we deduce the general condition under which point interactions have a substantial effect on statistical properties of the spectrum.
Katharina H. Kurth
2017-01-01
Full Text Available Polymer bonded magnets are compounds consisting of a polymer matrix with embedded hard magnetic filler particles. These materials are mainly used in applications in actor or sensor technology. One example is the application as multipolar encoder wheel in magnetic sensors. Depending on the application different requirements have to be fulfilled, such as a high pole length accuracy and repeatability. This investigation deals with the production of multipolar rings in the injection molding process for sensor applications and influences of the design of the gating system on the pole length accuracy. It is shown that the number of injection points and developing weld lines, as well as the positioning of the injection points, has a major influence on the magnetization characteristics of the molded rings. In general, a positioning of injection points and weld lines in the pole pitch and higher number of injection points lead to rings with a high reproduction accuracy of the pole length of the mold.
Qualitative behavior of a rational difference equation
Qian Xiao
2011-01-01
Full Text Available Abstract This article is concerned with the following rational difference equation yn+1 = (yn + yn-1/(p + ynyn-1 with the initial conditions; y-1, y0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated, and non-negative solution with prime period two cannot be found. Moreover, simulation is shown to support the results.
Y. Narita
2011-02-01
Full Text Available A new analysis method is presented that provides a high-resolution power spectrum in a broad wave number domain based on multi-point measurements. The analysis technique is referred to as the Multi-point Signal Resonator (MSR and it benefits from Capon's minimum variance method for obtaining the proper power spectral density of the signal as well as the MUSIC algorithm (Multiple Signal Classification for considerably reducing the noise part in the spectrum. The mathematical foundation of the analysis method is presented and it is applied to synthetic data as well as Cluster observations of the interplanetary magnetic field. Using the MSR technique for Cluster data we find a wave in the solar wind propagating parallel to the mean magnetic field with relatively small amplitude, which is not identified by the Capon spectrum. The Cluster data analysis shows the potential of the MSR technique for studying waves and turbulence using multi-point measurements.
Macmillan, C. J. B.
1985-01-01
The recognition of teaching as a special relationship among individuals is currently being overlooked in much contemporary educational research and policymaking. The author examines the philosophy of rationality in teaching and relates it to the educational vision presented in George Orwell's novel, "Nineteen Eighty-Four." (CB)
Lam, Chi-Ming
2014-01-01
Nowadays, there is still a widely held view that the Chinese and Western modes of thought are quite distinct from each other. In particular, the Chinese mode of thought derived from Confucianism is considered as comparatively less rational than the Western one. In this article, I first argue that although the analogical mode of argumentation,…
Harmening, Corinna; Neuner, Hans
2017-03-01
Freeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis. A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures. In [10] the problem of finding an alternative to these trial-and-error-procedures was addressed for the case of B-spline curves: The task of choosing the optimal number of control points was interpreted as a model selection problem. Two model selection criteria, the Akaike and the Bayesian Information Criterion, were used to identify the B-spline curve with the optimal number of control points from a set of candidate B-spline models. In order to overcome the drawbacks of the information criteria, an alternative approach based on statistical learning theory was developed. The criteria were evaluated by means of simulated data sets. The present paper continues these investigations. If necessary, the methods proposed in [10] are extended to areal approaches so that they can be used to determine the optimal number of B-spline surface control points. Furthermore, the methods are evaluated by means of real laser scanner data sets rather than by simulated ones. The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.
The Tipping Point: F-Score as a Function of the Number of Retrieved Items
Guns, Raf; Lioma, Christina; Larsen, Birger
2012-01-01
One of the best known measures of information retrieval (IR) performance is the F-score, the harmonic mean of precision and recall. In this article we show that the curve of the F-score as a function of the number of retrieved items is always of the same shape: a fast concave increase to a maximu...
Effects of number of events and relay point density on accuracy of three-dimensional AE-tomography
Kobayashi, Y.; Shiotani, T.; Oda, K.
2013-01-01
This paper introduces results of numerical investigations on accuracy of elastic wave velocity distribution in Three-dimensional AE-Tomography. A series of numerical analyses is conducted by changing number of events and density of relay points for the investigation. AE-Tomography is an identificati
Makki, Behrooz
2016-03-22
This paper investigates the performance of the point-To-point multiple-input-multiple-output (MIMO) systems in the presence of a large but finite numbers of antennas at the transmitters and/or receivers. Considering the cases with and without hybrid automatic repeat request (HARQ) feedback, we determine the minimum numbers of the transmit/receive antennas, which are required to satisfy different outage probability constraints. Our results are obtained for different fading conditions and the effect of the power amplifiers efficiency/feedback error probability on the performance of the MIMO-HARQ systems is analyzed. Then, we use some recent results on the achievable rates of finite block-length codes, to analyze the effect of the codewords lengths on the system performance. Moreover, we derive closed-form expressions for the asymptotic performance of the MIMO-HARQ systems when the number of antennas increases. Our analytical and numerical results show that different outage requirements can be satisfied with relatively few transmit/receive antennas. © 1972-2012 IEEE.
Georg Spielthenner
2007-01-01
Full Text Available Valuations are ubiquitous. We may be for or against genetically modified food; we find some politicians irresponsible; we prefer Beethoven to rock ‘n’ roll or vice versa; some enjoy bird-watching while others find it boring; and we may think that we have to tighten up on green-house gas emissions. Valuing is pervasive and often we are not even aware that we are valuing. However, many of ourvaluations are ill grounded and rationally defective. They are frequently based on misinformation, sloppy thinking, prejudice, and are biased in many ways as psychological research shows. For this reason there is widespread agreement among phi-losophers that we need an account of substantive valuational rationality, both for the theory of practical reasoning and for ethics as well. My main objectin this paper is to outline such an account and to present a principle that allows a non-technical rational criticism of valuations
Ballester Pla, Coralio
2012-03-01
Full Text Available The observation of the actual behavior by economic decision makers in the lab and in the field justifies that bounded rationality has been a generally accepted assumption in many socio-economic models. The goal of this paper is to illustrate the difficulties involved in providing a correct definition of what a rational (or irrational agent is. In this paper we describe two frameworks that employ different approaches for analyzing bounded rationality. The first is a spatial segregation set-up that encompasses two optimization methodologies: backward induction and forward induction. The main result is that, even under the same state of knowledge, rational and non-rational agents may match their actions. The second framework elaborates on the relationship between irrationality and informational restrictions. We use the beauty contest (Nagel, 1995 as a device to explain this relationship.
La observación del comportamiento de los agentes económicos tanto en el laboratorio como en la vida real justifica que la racionalidad acotada sea un supuesto aceptado en numerosos modelos socio-económicos. El objetivo de este artículo es ilustrar las dificultades que conlleva una correcta definición de qué es un agente racional (irracional. En este artículo se describen dos marcos que emplean diferentes metodologías para analizar la racionalidad acotada. El primero es un modelo de segregación espacial donde se contrastan dos metodologías de optimización: inducción hacia atrás y hacia adelante. El resultado principal es que, incluso con el mismo nivel de conocimiento, tanto agentes racionales como irracionales podrían coincidir en sus acciones. El segundo marco trabaja sobre la relación entre irracionalidad y restricción de información. Se utiliza el juego llamado “beauty contest” (Nagel 1995 como mecanismo para explicar dicha relación.
Long-term trends of magnetic bright points: I. Number of MBPs at disc centre
Utz, D; Thonhofer, S; Veronig, A; Hanslmeier, A; Bodnárová, M; Bárta, M; Iniesta, J C del Toro
2015-01-01
Context. The Sun shows an activity cycle that is caused by its varying global magnetic field. During a solar cycle, sunspots, i.e. extended regions of strong magnetic fields, occur in activity belts that are slowly migrating from middle to lower latitudes, finally arriving close to the equator during the cycle maximum phase. While this have been well known for centuries, much less is known about the solar cycle evolution of small-scale magnetic fields. Aims. To address this question, we study magnetic bright points (MBPs) as proxies for such small-scale, kG solar magnetic fields. This study is based on a homogeneous data set that covers a period of eight years. Methods. An automated MBP identification algorithm was applied to the synoptic Hinode/SOT G-band data over the period November 2006 to August 2014, i.e. covering the decreasing phase of Cycle 23 and the rise, maximum, and early decrease of Cycle 24. This data set includes, at the moment of investigation, a total of 4 162 images, with about 2.9 million ...
Construction of `Wachspress Type' Rational Basis Functions over Rectangles
P L Powar; S S Rana
2000-02-01
In the present paper, we have constructed rational basis functions of 0 class over rectangular elements with wider choice of denominator function. This construction yields additional number of interior nodes. Hence, extra nodal points and the flexibility of denominator function suggest better approximation.
Binmore, Ken
2008-01-01
It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to ""look before you leap."" If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics,
Boskovic, Goran; Jovicic, Nebojsa
2015-12-01
This paper concerns the development of a methodology aimed at determining the optimal number of waste bins as well optimizing the location of collection points. The methodology was based on a geographic information system, which handled different sets of information, such as street directions, spatial location of objects and number of inhabitants, location of waste bins, and radius of their coverage. The study was conducted in a district in the central area of the city of Kragujevac. Due to a lack of information about the existing situation, all necessary data was collected by fieldwork and by using GPS equipment. By using the developed methodology, the results indicated a reduction of 24% in the number of collection points and 33.5% in the number of waste bins, without reducing the quality of the provided services. It has led to cost and time savings for waste collection and environmental benefits. All users of the services were covered within a 75-m radius, and the usage of bins is more efficient. According to the reduction in the number of waste bins, a total amount of €26,000 may be achieved. In addition, the time for waste collection was reduced, resulting in a €1700 saving per year in fuel costs, as well as 4.5 tons of emitted CO2 into the atmosphere. © The Author(s) 2015.
Cetina, M; Leaños, J; Villalobos, C
2010-01-01
There are two properties shared by all known crossing-minimizing geometric drawings of $K_n$, for $n$ a multiple of $3$. First, the underlying $n$-point set of these drawings has exactly $3\\binom{k+2}{2}$ $(\\le k)$-edges, for all $0\\le k < n/3$. Second, all such drawings have the $n$ points divided into three groups of equal size; this last property is captured under the concept of $3$-decomposability. In this paper we show that these properties are tightly related: every $n$-point set with exactly $3\\binom{k+2}{2}$ $(\\le k)$-edges for all $0\\le k < n/3$, is $3$-decomposable. As an application, we prove that the rectilinear crossing number of $K_{30}$ is $9726$.
Fukushima, Toshio
2012-04-01
By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated Legendre functions (ALF) by recursion without underflow problem. The new method enables us to evaluate ALFs of extremely high degree as 232 = 4,294,967,296, which corresponds to around 1 cm resolution on the Earth's surface. By limiting the application of exponent extension to a few working variables in the recursion, choosing a suitable large power of 2 as the radix, and embedding the contents of the basic arithmetic procedure of floating point numbers with the exponent extension directly in the program computing the recurrence formulas, we achieve the evaluation of ALFs in the double-precision environment at the cost of around 10% increase in computational time per single ALF. This formulation realizes meaningful execution of the spherical harmonic synthesis and/or analysis of arbitrary degree and order.
无
2009-01-01
We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.
ZHANG Yu; HOU ZhanFeng; LIU YuXin
2009-01-01
We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and Isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.
Mambrini, Y.; Moultaka, G.
2001-01-01
We reconsider the Infrared Quasi Fixed Points which were studied recently in the literature in the context of the Baryon and Lepton number violating Minimal Supersymmetric Standard Model (hep-ph/0011274). The complete analysis requires further care and reveals more structure than what was previously shown. The formalism we develop here is quite general, and can be readily applied to a large class of models.
Rationalization: A Bibliography.
Pedrini, D. T.; Pedrini, Bonnie C.
Rationalization was studied by Sigmund Freud and was specifically labeled by Ernest Jones. Rationalization ought to be differentiated from rational, rationality, logical analysis, etc. On the one hand, rationalization is considered a defense mechanism, on the other hand, rationality is not. Haan has done much work with self-report inventories and…
Rational inattention or rational overreaction?
Browning, Martin; Hansen, Lars Gårn; Smed, Sinne
We investigate differences in how consumers of fish react to health information in the mass media. We specify a dynamic empirical model that allows for heterogeneity in all basic parameters of consumer behavior as well as in how consumers react to information. We estimate the model using a unique...... houshold panel tracking consumption, prices, news stories and media habits over 24 quarters. We fi nd that the consumers most likely to be ’rationally ignorant’ of health effects react more dramatically to health news than the consumers who most likely are well informed....
Rational inattention or rational overreaction?
Browning, Martin; Hansen, Lars Gårn; Smed, Sinne
We investigate differences in how consumers of fish react to health information in the mass media. We specify a dynamic empirical model that allows for heterogeneity in all basic parameters of consumer behavior as well as in how consumers react to information. We estimate the model using a unique...... houshold panel tracking consumption, prices, news stories and media habits over 24 quarters. We fi nd that the consumers most likely to be ’rationally ignorant’ of health effects react more dramatically to health news than the consumers who most likely are well informed....
Rational offset approximation of rational Bézier curves
CHENG Min; WANG Guo-jin
2006-01-01
The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented.
Lee, Romeo B; Baring, Rito V; Sta Maria, Madelene A
2016-02-01
The study seeks to estimate gender variations in the direct effects of (a) number of organizational memberships, (b) number of social networking sites (SNS), and (c) grade-point average (GPA) on global social responsibility (GSR); and in the indirect effects of (a) and of (b) through (c) on GSR. Cross-sectional survey data were drawn from questionnaire interviews involving 3,173 Filipino university students. Based on a path model, the three factors were tested to determine their inter-relationships and their relationships with GSR. The direct and total effects of the exogenous factors on the dependent variable are statistically significantly robust. The indirect effects of organizational memberships on GSR through GPA are also statistically significant, but the indirect effects of SNS on GSR through GPA are marginal. Men and women significantly differ only in terms of the total effects of their organizational memberships on GSR. The lack of broad gender variations in the effects of SNS, organizational memberships and GPA on GSR may be linked to the relatively homogenous characteristics and experiences of the university students interviewed. There is a need for more path models to better understand the predictors of GSR in local students.
Woronowicz, Michael
2016-11-01
Analytical expressions for column number density (CND) are developed for optical line of sight paths through a variety of steady free molecule point source models including directionally-constrained effusion (Mach number M = 0) and flow from a sonic orifice (M = 1). Sonic orifice solutions are approximate, developed using a fair simulacrum fitted to the free molecule solution. Expressions are also developed for a spherically-symmetric thermal expansion (M = 0). CND solutions are found for the most general paths relative to these sources and briefly explored. It is determined that the maximum CND from a distant location through directed effusion and sonic orifice cases occurs along the path parallel to the source plane that intersects the plume axis. For the effusive case this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plume's axis. For sonic plumes this ratio is reduced to about 4/3. For high Mach number cases the maximum CND will be found along the axial centerline path.
Woronowicz, Michael S.
2016-01-01
Analytical expressions for column number density (CND) are developed for optical line of sight paths through a variety of steady free molecule point source models including directionally-constrained effusion (Mach number M = 0) and flow from a sonic orifice (M 1). Sonic orifice solutions are approximate, developed using a fair simulacrum fitted to the free molecule solution. Expressions are also developed for a spherically-symmetric thermal expansion (M = 0). CND solutions are found for the most general paths relative to these sources and briefly explored. It is determined that the maximum CND from a distant location through directed effusion and sonic orifice cases occurs along the path parallel to the source plane that intersects the plume axis. For the effusive case this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plumes axis. For sonic plumes this ratio is reduced to about 43. For high Mach number cases the maximum CND will be found along the axial centerline path.
Fukushima, Toshio
2014-02-01
The integrals of fully normalized associated Legendre function (fnALF) of extremely high degree and order such as 223=8 388 608 can be obtained without underflow problems if the point values of fnALF are properly given by using an exponent extension of the floating point numbers (Fukushima, T., 2012a. J. Geod., 86, 271-285; Fukushima, T., 2012c. J. Geod., 86, 1019-1028). A dynamic termination of the exponent extension during the fixed-order increasing-degree recursions significantly reduces the increase in CPU time caused by the exponent extension. Also, the sectorial integrals are found to be correctly obtained by the forward recursion only even when the backward recursion has been claimed to be necessary (Paul, M.K., 1978, Bull. Geod., 52, 177-190; Gerstl, M., 1980, Manuscr. Geod., 5, 181-199).
Bolsunov, A. A.; Karpov, S. A.
2013-12-01
An algorithm for refining the differential characteristics of the control rods (CRs) of the control and protection system (CPS) for a neutronics model of the VVER-1000 simulator at a low number of axial mesh points of the core is described. The problem of determining the constants for a cell with a partially inserted CR is solved. The cell constants obtained using the proposed approach ensure smoothing of the differential characteristics of an absorbing rod. The algorithm was used in the VVER-1000 simulators (Bushehr NPP, unit no. 1; Rostov NPP, unit no. 1; and Balakovo NPP, unit no. 4).
孙慧
2015-01-01
研究了通过未定元替换应用Eisenstein判别法的等价条件，并借鉴Eisenstein判别法的研究思路，给出了一类整系数多项式在有理数域上不可约的判别方法。%The equivalent conditions of Eisenstein discriminant method to replace the of application by in-finite element x was studied .The train thought of Eisenstein discriminant method was used in the study .A class of integral coefficients polynomial was given on the rational number field irreducible discriminant method .
Angeles, Jorge
1988-01-01
A rational study of kinematics is a treatment of the subject based on invariants, i.e., quantities that remain essentially unchanged under a change of observer. An observer is understood to be a reference frame supplied with a clock (Truesdell 1966). This study will therefore include an introduction to invariants. The language of these is tensor analysis and multilinear algebra, both of which share many isomorphic relations, These subjects are treated in full detail in Ericksen (1960) and Bowen and Wang (1976), and hence will not be included here. Only a short account of notation and definitions will be presented. Moreover, definitions and basic concepts pertaining to the kinematics of rigid bodies will be also included. Although the kinematics of rigid bodies can be regarded as a particular case of the kinematics of continua, the former deserves attention on its own merits for several reasons. One of these is that it describes locally the motions undergone by continua. Another reason is that a whole area of ...
Popper, Rationality and the Possibility of Social Science
Danny Frederick
2013-02-01
Full Text Available Social science employs teleological explanations which depend upon the rationality principle, according to which people exhibit instrumental rationality. Popper points out that people also exhibit critical rationality, the tendency to stand back from, and to question or criticise, their views. I explain how our critical rationality impugns the explanatory value of the rationality principle and thereby threatens the very possibility of social science. I discuss the relationship between instrumental and critical rationality and show how we can reconcile our critical rationality with the possibility of social science if we invoke Popper’s conception of limited rationality and his indeterminism.
Silvia Erina
2012-10-01
Full Text Available The study was carried out on 9 Romanian Black and White primiparous cows. The aim of this study was todetermine some aspect of nutritional behaviour of the cows. During the experiments, the following behaviour aspectswere determined: interruption number and their duration in the feed consumption time. Results showed that theadministration order of forages had an influence on the interruptions number, which was 0.74 less for hay in fibroussucculentorder (O1. For silage, the interruption number was 0.42 higher in fibrous-succulent order (O1. Betweenportion 1 (P1 and portion 3 (P3, the significant difference (p<0.05 was for interruptions duration, duringconsumption silage, in favour portion P1. Distinct significant differences (p<0.01 was observed for the interruptionnumber during consumption silage (0.95 sec. higher in P1 than in P3, for interruption duration (5.96 sec. higher inP1 than in P3. Between P2 and P3, significant difference (p<0.05 was observed for interruptions number duringconsumption silage and for average interruptions duration during consumption beet in favour to portion P2.Regarding the number of feedings per portion, always the differences were higher in the second feeding F1 than inthe first feeding F2.
Woronowicz, Michael
2017-01-01
Providers of payloads carried aboard the International Space Station must conduct analyses to demonstrate that any planned gaseous venting events generate no more than a certain level of material that may interfere with optical measurements from other experiments or payloads located nearby. This requirement is expressed in terms of a maximum column number density (CND). Depending on the level of rarefaction, such venting may be characterized by effusion for low flow rates, or by a sonic distribution at higher levels. Since the relative locations of other sensitive payloads are often unknown because they may refer to future projects, this requirement becomes a search for the maximum CND along any path.In another application, certain astronomical observations make use of CND to estimate light attenuation from a distant star through gaseous plumes, such as the Fermi Bubbles emanating from the vicinity of the black hole at the center of our Milky Way galaxy, in order to infer the amount of material being expelled via those plumes.This paper presents analytical CND expressions developed for general straight paths based upon a free molecule point source model for steady effusive flow and for a distribution fitted to model flows from a sonic orifice. Among other things, in this Mach number range it is demonstrated that the maximum CND from a distant location occurs along the path parallel to the source plane that intersects the plume axis. For effusive flows this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plumes axis. For sonic plumes this ratio is reduced to about 43.
Maxted, Jeffrey T; Diebel, Matthew W; Vander Zanden, M Jake
2009-01-01
Agricultural non-point source (NPS) pollution poses a severe threat to water quality and aquatic ecosystems. In response, tremendous efforts have been directed toward reducing these pollution inputs by implementing agricultural conservation practices. Although conservation practices reduce pollution inputs from individual fields, scaling pollution control benefits up to the watershed level (i.e., improvements in stream water quality) has been a difficult challenge. This difficulty highlights the need for NPS reduction programs that focus efforts within target watersheds and at specific locations within target watersheds, with the ultimate goal of improving stream water quality. Fundamental program design features for NPS control programs--i.e., number of watersheds in the program, total watershed area, and level of effort expended within watersheds--have not been considered in any sort of formal analysis. Here, we present an optimization model that explores the programmatic and environmental trade-offs between these design choices. Across a series of annual program budgets ranging from $2 to $200 million, the optimal number of watersheds ranged from 3 to 27; optimal watershed area ranged from 29 to 214 km(2); and optimal expenditure ranged from $21,000 to $35,000/km(2). The optimal program configuration was highly dependent on total program budget. Based on our general findings, we delineated hydrologically complete and spatially independent watersheds ranging in area from 20 to 100 km(2). These watersheds are designed to serve as implementation units for a targeted NPS pollution control program currently being developed in Wisconsin.
Kuhlman, John M.; Liaw, Paul; Cerney, Michael J.
1988-01-01
A numerical design study was conducted to assess the drag reduction potential of winglets installed on a series of low aspect ratio wings at a design point of M=0.8, C sub L=0.3. Wing-winglet and wing-alone design geometries were obtained for wings of aspect ratios between 1.75 and 2.67, having leading edge sweep angles between 45 and 60 deg. Winglet length was fixed at 15% of wing semispan. To assess the relative performance between wing-winglet and wing-alone configurations, the PPW nonlinear extended small disturbance potential flow code was utilized. This model has proven to yield plausible transonic flow field simulations for the series of low aspect ratio configurations selected. Predicted decreases in pressure drag coefficient for the wing-winglet configurations relative to the corresponding wing-alone planform are about 15% at the design point. Predicted decreases in wing-winglet total drag coefficient are about 12%, relative to the corresponding wing-alone design. Longer winglets (25% of the wing semispan) yielded decreases in the pressure drag of up to 22% and total drag of up to 16.4%. These predicted drag coefficient reductions are comparable to reductions already demonstrated by actual winglet designs installed on higher aspect ratio transport type aircraft.
Saldana, D A; Starck, L; Mougin, P; Rousseau, B; Creton, B
2013-01-01
We report the development of predictive models for two fuel specifications: melting points (T(m)) and net heat of combustion (Δ(c)H). Compounds inside the scope of these models are those likely to be found in alternative fuels, i.e. hydrocarbons, alcohols and esters. Experimental T(m) and Δ(c)H values for these types of molecules have been gathered to generate a unique database. Various quantitative structure-property relationship (QSPR) approaches have been used to build models, ranging from methods leading to multi-linear models such as genetic function approximation (GFA), or partial least squares (PLS) to those leading to non-linear models such as feed-forward artificial neural networks (FFANN), general regression neural networks (GRNN), support vector machines (SVM), or graph machines. Except for the case of the graph machines method for which the only inputs are SMILES formulae, previously listed approaches working on molecular descriptors and functional group count descriptors were used to develop specific models for T(m) and Δ(c)H. For each property, the predictive models return slightly different responses for each molecular structure. Therefore, models labelled as 'consensus models' were built by averaging values computed with selected individual models. Predicted results were then compared with experimental data and with predictions of models in the literature.
Rationality of trace and norm L-functions
Rojas-León, Antonio
2010-01-01
For a given l-adic sheaf F on the affine line A^1 over a finite field k (respectively on the torus G_m) and an positive integer r we define the r-th local trace L-function of F at a point t of k (resp. its local norm L-function at a non-zero t in k) and prove its rationality. This function gives information on the sum of the local Frobenius traces of F over the points of k_r (the extension of degree r of k) with trace t (resp. with norm t). These sums can in turn be used to estimate the number of rational points on curves or the absolute value of exponential sums which are invariant under a large group of translations or homotheties.
刘香坤; 姬玉梅
2011-01-01
With the theory of unascertained rational number, a kind of evaluation model on adjustment of agricultural production structure was established combined with the actual situation of adjustment of agricultural production structure. The model could be used to quantitatively study the effect of adjustment of agricultural production structure.%利用未确知有理数理论,结合农业生产结构调整的实际情况,建立了一种评价农业生产结构调整的模型,该模型可用于定量研究农业生产结构调整的效果.
On rationally supported surfaces
Gravesen, Jens; Juttler, B.; Sir, Z.
2008-01-01
We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions....... In particular it is shown that odd rational support functions correspond to those rational surfaces which can be equipped with a linear field of normal vectors, which were discussed by Sampoli et al. (Sampoli, M.L., Peternell, M., Juttler, B., 2006. Rational surfaces with linear normals and their convolutions...... with rational surfaces. Comput. Aided Geom. Design 23, 179-192). As shown recently, this class of surfaces includes non-developable quadratic triangular Bezier surface patches (Lavicka, M., Bastl, B., 2007. Rational hypersurfaces with rational convolutions. Comput. Aided Geom. Design 24, 410426; Peternell, M...
Public policy, rationality and reason
Rodolfo Canto Sáenz
2015-07-01
Full Text Available This work suggests the incorporation of practical reason in the design, implementation and evaluation of public policies, alongside instrumental rationality. It takes two proposals that today point in this direction: Rawls distinction between reasonable (practical reason and rational (instrumental reason and what this author calls the CI Procedure (categorical imperative procedure and Habermas model of deliberative democracy. The main conclusion is that the analysis of public policies can not be limited to rather narrow limits of science, but requires the contribution of political and moral philosophy.
Change in Number and Types of Postsecondary Institutions: 2000 to 2014. Data Point. NCES 2017-008
Hudson, Lisa
2017-01-01
This Data Point uses data from the Integrated Postsecondary Education Data System (IPEDS). IPEDS is an annual data collection of all postsecondary institutions in the United States and outlying territories that participate in Title IV federal student financial aid programs. This Data Point presents IPEDS data for U.S. undergraduate institutions in…
Using rational numbers to key nested sets
Hazel, Dan
2008-01-01
This report details the generation and use of tree node ordering keys in a single relational database table. The keys for each node are calculated from the keys of its parent, in such a way that the sort order places every node in the tree before all of its descendants and after all siblings having a lower index. The calculation from parent keys to child keys is simple, and reversible in the sense that the keys of every ancestor of a node can be calculated from that node's keys without having to consult the database. Proofs of the above properties of the key encoding process and of its correspondence to a finite continued fraction form are provided.
Hougaard, Jens Leth; Moreno-Ternero, Juan D.; Østerdal, Lars Peter Raahave
2013-01-01
We introduce a new operator for general rationing problems in which, besides conflicting claims, individual baselines play an important role in the rationing process. The operator builds onto ideas of composition, which are not only frequent in rationing, but also in related problems...... such as bargaining, choice, and queuing. We characterize the operator and show how it preserves some standard axioms in the literature on rationing. We also relate it to recent contributions in such literature....
Love and rationality: on some possible rational effects of love
Gustavo Ortiz-Millán
Full Text Available In this paper I defend the idea that rather than disrupting rationality, as the common-sense conception has done it, love may actually help us to develop rational ways of thinking and acting. I make the case for romantic or erotic love, since this is the kind of love that is more frequently associated with irrationality in acting and thinking. I argue that this kind of love may make us develop epistemic and practical forms of rationality. Based on an analysis of its characteristic action tendencies, I argue that love may help us to develop an instrumental form of rationality in determining the best means to achieve the object of love. It may also narrow down the number of practical considerations that may help us to achieve our goals. Finally, love may generate rational ways of belief-formation by framing the parameters taken into account in perception and attention, and by bringing into light only a small portion of the epistemic information available. Love may make us perceive reality more acutely.
Binomial Squares in Pure Cubic Number Fields
Lemmermeyer, Franz
2011-01-01
Let K = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m.
Integral points in two-parameter orbits
Corvaja, Pietro; Tucker, Thomas J; Zannier, Umberto
2012-01-01
Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of degree greater than 1, let S be a finite set of places of K, and suppose that u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively computable. This may be thought of as a two-parameter analog of a result of Silverman on integral points in orbits of rational maps. This issue can be translated in terms of integral points on an open subset of P_1^2; then one can apply a modern version of the method of Runge, after increasing the number of components at infinity by iterating the rational map. Alternatively, an ineffective result comes from a well-known theorem of Vojta.
Sadi, M; Dabir, B
2003-01-01
Monte Carlo Method is one of the most powerful techniques to model different processes, such as polymerization reactions. By this method, without any need to solve moment equations, a very detailed information on the structure and properties of polymers are obtained. The number of algorithm repetitions (selected volumes of reactor for modelling which represent the number of initial molecules) is very important in this method. In Monte Carlo method calculations are based on the random number of generations and reaction probability determinations. so the number of algorithm repetition is very important. In this paper, the initiation reaction was considered alone and the importance of number of initiator molecules on the result were studied. It can be concluded that Monte Carlo method will not give accurate results if the number of molecules is not satisfied to be big enough, because in that case , selected volume would not be representative of the whole system.
Walker, Janet S., Ed.
2005-01-01
This issue of "Focal Point" explores the concepts of resilience and recovery and what they mean in the context of mental health care for children and adolescents. From the articles, it emerges that the terminology associated with recovery and resilience (particularly the word, recovery, itself) can be confusing and even off-putting to…
Stability and convergence of a higher order rational difference Equation
Gazor, Hamid
2011-01-01
In this paper the asymptotic stability of equilibria and periodic points of the following higher order rational difference Equation x_{n+1} =(alpha x_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters ?alpha, betta, and gamma are positive real numbers, and the initial conditions x_{-k}, ..., x_{0} are given arbitrary real numbers. The forbidden set of this equation is found and then, the order reduction method is used to facilitate the analysis of its asymptotic dynamics
Perturbing rational harmonic functions by poles
Sète, Olivier; Liesen, Jörg
2014-01-01
We study how adding certain poles to rational harmonic functions of the form $R(z)-\\bar{z}$, with $R(z)$ rational and of degree $d\\geq 2$, affects the number of zeros of the resulting functions. Our results are motivated by and generalize a construction of Rhie derived in the context of gravitational microlensing (ArXiv e-print 2003). Of particular interest is the construction and the behavior of rational functions $R(z)$ that are {\\em extremal} in the sense that $R(z)-\\bar{z}$ has the maximal possible number of $5(d-1)$ zeros.
Zwietering, M.H.; Wit, de J.C.; Notermans, S.
1996-01-01
A procedure is presented to quantitatively estimate the growth of a particular organism in a food product during chilled storage using predictive microbiology. This results in a quantification of the contribution of every individual process step to the total number of organisms, which may be a usefu
Simple Equational Specifications of Rational Arithmetic
Lawrence S. Moss
2001-12-01
Full Text Available We exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers. It uses one hidden function; that function is unary. But it does not use an error constant, or extra (hidden sorts, or conditional equations. All of our work is elementary and self-contained.
Determinants of Actor Rationality
Ellegaard, Chris
Industrial companies must exercise influence on their suppliers (or supplier actors). Actor rationality is a central theme connected to this management task. In this article, relevant literature is studied with the purpose of shedding light on determinants of actor rationality. Two buyer......-supplier relations are investigated in a multiple case study, leading to the proposal of various additional factors that determine and shape actor rationality. Moreover a conceptual model of rationality determinants in the buyer-supplier relation is proposed, a model that may help supply managers analyse...
老年人合理驾驶方式研究切入点探讨%A Starting Point of the Study for Senior People’s Rational Driving Styles
杨浩
2015-01-01
This study is from the perspective of product design. The author tries to ifnd out a decent starting point for the complicated senior people’s driving styles research. Based on driving needs of the aged in modern phase, the paper analyzes the necessity and opportunities of senior-oriented individual motorized vehicles. Senior people have their specialties in reaction and limb’s functions. Thus to some extent the mainstream vehicles that aims at serving for the youth are not suitable for modern Chinese senior generation. The study makes senior people’s driving behavior characteristics as a starting point, and analyzes three motorized vehicles which are popular among Chinese senior people. Comparison is made and feasible design is proposed. The study can be seemed as a rational research hypothesis for the senior people’s driving styles research.%本文从产品设计视角出发，力求为复杂的老年人驾驶方式研究寻找到合适的切入点，为老年人交通工具设计提供有力支持。文章基于现阶段老年人自驾需求，分析了面向老年人的个人机动车市场的必要性及发展契机。老年人在反应特征和肢体机能上有其特殊性，因此以年轻人为主要消费对象的主流机动车辆在很大程度上并不适合当代中国老年人驾驶。文章以老年人驾驶操作特点为切入点，分析了几种颇受老年人欢迎的机动车辆的驾驶方式，并进行比较、提出了可行性方案，为老年人合理驾驶方式的研究提出了合理的研究假设。
There are Infinitely many Limit Points of the Fractional Parts of Powers
Artūras Dubickas
2005-11-01
Suppose that > 1 is an algebraic number and $ > 0$ is a real number. We prove that the sequence of fractional parts $\\{^n\\},n=1,2,3,\\ldots,$ has infinitely many limit points except when is a PV-number and $\\in\\mathbb{Q}()$. For =1 and being a rational non-integer number, this result was proved by Vijayaraghavan.
Height Estimates for Equidimensional Dominant Rational Maps
Silverman, Joseph H
2009-01-01
Let F : W --> V be a dominant rational map between quasi-projective varieties of the same dimension. We give two proofs that h_V(F(P)) >> h_W(P) for all points P in a nonempty Zariski open subset of W. For dominant rational maps F : P^n --> P^n, we give a uniform estimate in which the implied constant depends only on n and the degree of F. As an application, we prove a specialization theorem for equidimensional dominant rational maps to semiabelian varieties, providing a complement to Habegger's recent theorem on unlikely intersections.
Vorob'ev, Nikolai Nikolaevich
2011-01-01
Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the ""golden section"" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teacher
Standby Gasoline Rationing Plan
None
1980-06-01
The final rules adopted by the President for a Standby Gasoline Rationing Plan are presented. The plan provides that eligibility for ration allotments will be determined primarily on the basis of motor vehicle registrations, taking into account historical differences in the use of gasoline among states. The regulations also provide authority for supplemental allotments to firms so that their allotment will equal a specified percentage of gasoline use during a base period. Priority classifications, i.e., agriculture, defense, etc., are established to assure adequate gasoline supplies for designated essential services. Ration rights must be provided by end-users to their suppliers for each gallon sold. DOE will regulate the distribution of gasoline at the wholesale level according to the transfer by suppliers of redeemed ration rights and the gasoline allocation regulations. Ration rights are transferable. A ration banking system is created to facilitate transfers of ration rights. Each state will be provided with a reserve of ration rights to provide for hardship needs and to alleviate inequities. (DC)
Implicitization of rational maps
Botbol, Nicolas
2011-01-01
Motivated by the interest in computing explicit formulas for resultants and discriminants initiated by B\\'ezout, Cayley and Sylvester in the eighteenth and nineteenth centuries, and emphasized in the latest years due to the increase of computing power, we focus on the implicitization of hypersurfaces in several contexts. Our approach is based on the use of linear syzygies by means of approximation complexes, following [Bus\\'e Jouanolou 03], where they develop the theory for a rational map $f:P^{n-1}\\dashrightarrow P^n$. Approximation complexes were first introduced by Herzog, Simis and Vasconcelos in [Herzog Simis Vasconcelos 82] almost 30 years ago. The main obstruction for this approximation complex-based method comes from the bad behavior of the base locus of $f$. Thus, it is natural to try different compatifications of $A^{n-1}$, that are better suited to the map $f$, in order to avoid unwanted base points. With this purpose, in this thesis we study toric compactifications $T$ for $A^{n-1}$. We provide re...
Irrational Rationality of Terrorism
Robert Nalbandov
2013-12-01
Full Text Available The present article deals with the ontological problem of applying the rational choice frameworks to the study of terrorism. It testing the application of the rational choice to the “old” (before the end of the Cold War and the “new” (after the end of the Cold War terrorisms. It starts with analyzing the fundamentals of rationality and applies it at two levels: the individual (actors and group (collective via two outlooks: tactical (short-term and strategic (long-term. The main argument of the article is that while the “old” terrorism can be explained by the rational choice theory its “new” version represents a substantial departure from rationality.
Percents Are Not Natural Numbers
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Exploring rationality in schizophrenia
Revsbech, Rasmus; Mortensen, Erik Lykke; Owen, Gareth
2015-01-01
Background Empirical studies of rationality (syllogisms) in patients with schizophrenia have obtained different results. One study found that patients reason more logically if the syllogism is presented through an unusual content. Aims To explore syllogism-based rationality in schizophrenia. Method...... Thirty-eight first-admitted patients with schizophrenia and 38 healthy controls solved 29 syllogisms that varied in presentation content (ordinary v. unusual) and validity (valid v. invalid). Statistical tests were made of unadjusted and adjusted group differences in models adjusting for intelligence...... differences became non-significant. Conclusions When taking intelligence and neuropsychological performance into account, patients with schizophrenia and controls perform similarly on syllogism tests of rationality....
RATIONAL SOLUTIONS FOR DEVELOPMENT OF TELECOMMUNICATIONS NETWORKS
Sokolov, A.; Sokolov, N.
2014-01-01
The number of complicated problems has to be solved during modernization of the telecommunication networks. Some problems can be defined as a search for rational solutions instead of the traditional approach that consists in finding the cost function optimum. This new approach minimizes the risk that inevitably arises when elaborating a long term plan for the telecommunication networks development. The article discusses the proposed methodological approach of finding rational solutions. Probl...
A quantitative estimate for quasi-integral points in orbits
Hsia, Liang-Chung
2009-01-01
Let f(z) be a rational function of degree at least 2 with coefficients in a number field K, and assume that the second iterate f^2(z) of f(z) is not a polynomial. The second author previously proved that for any b in K, the forward orbit O_f(b) contains only finitely many quasi-S-integral points. In this note we give an explicit upper bound for the number of such points.
Information, Utility & Bounded Rationality
Ortega, Pedro A
2011-01-01
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we employ an axiomatic framework for bounded rational decision-making based on a thermodynamic interpretation of resource costs as information costs. This leads to a variational "free utility" principle akin to thermodynamical free energy that trades off utility and information costs. We show that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies. Furthermore, we show that risk-sensitive and robust (minimax) control schemes fall out naturally from this framework if the environment is considered as a bounded rational and perfectly rational opponent, respectively. When resource costs are ignored, the maximum expected utility principle is recovered.
Uncertainty, rationality, and agency
Hoek, Wiebe van der
2006-01-01
Goes across 'classical' borderlines of disciplinesUnifies logic, game theory, and epistemics and studies them in an agent-settingCombines classical and novel approaches to uncertainty, rationality, and agency
Crab Rationalization Permit Program
National Oceanic and Atmospheric Administration, Department of Commerce — The Crab Rationalization Program (Program) allocates BSAI crab resources among harvesters, processors, and coastal communities. The North Pacific Fishery Management...
Janusz J. Charatonik
1994-05-01
Full Text Available Spaces which are metrizable completions of the space Q of rationals are described. A characterization of metrizable spaces having the same family of metrizable completions as Q is deduced.
[Concepts of rational taxonomy].
Pavlinov, I Ia
2011-01-01
The problems are discussed related to development of concepts of rational taxonomy and rational classifications (taxonomic systems) in biology. Rational taxonomy is based on the assumption that the key characteristic of rationality is deductive inference of certain partial judgments about reality under study from other judgments taken as more general and a priory true. Respectively, two forms of rationality are discriminated--ontological and epistemological ones. The former implies inference of classifications properties from general (essential) properties of the reality being investigated. The latter implies inference of the partial rules of judgments about classifications from more general (formal) rules. The following principal concepts of ontologically rational biological taxonomy are considered: "crystallographic" approach, inference of the orderliness of organismal diversity from general laws of Nature, inference of the above orderliness from the orderliness of ontogenetic development programs, based on the concept of natural kind and Cassirer's series theory, based on the systemic concept, based on the idea of periodic systems. Various concepts of ontologically rational taxonomy can be generalized by an idea of the causal taxonomy, according to which any biologically sound classification is founded on a contentwise model of biological diversity that includes explicit indication of general causes responsible for that diversity. It is asserted that each category of general causation and respective background model may serve as a basis for a particular ontologically rational taxonomy as a distinctive research program. Concepts of epistemologically rational taxonomy and classifications (taxonomic systems) can be interpreted in terms of application of certain epistemological criteria of substantiation of scientific status of taxonomy in general and of taxonomic systems in particular. These concepts include: consideration of taxonomy consistency from the
Controllability under rational expectations.
Hughes Hallett Andrew; Di Bartolomeo Giovanni; Acocella Nicola
2008-01-01
We show that rational expectations do not affect the controllability of an economic system, either in its static or in its dynamic version, even though their introduction in many other circumstances may make it impossible for the policymaker to affect certain variables due to policy invariance, policy neutrality or time inconsistency problems. The controllability conditions stated by Tinbergen and subsequent authors continue to hold under rational expectations; and when they are satisfied rat...
Phronesis – hermeneutic rationality
Michał Januszkiewicz
2016-01-01
The paper is an attempt to rethink the problem of rationality in the humanities in the context of hermeneutics. The author argues that this concept of rationality must be founded on the Aristotelian concept of practical reason (phronesis). Phronesis is a need for discernment of the self or rather to find itself in its own, tangible, specific situation. This understanding concerns Being-inthe-world and belongs to what in Martin Heidegger’s ontohermeneutics we can determine precisely as underst...
Proposed standby gasoline rationing plan: public comments
1978-12-01
Under the proposed plan, DOE would allocate ration rights (rights to purchase gasoline) to owners of registered vehicles. All vehicles in a given class would receive the same entitlement. Essential services would receive supplemental allotments of ration rights as pririty firms. Once every 3 months, ration checks would be mailed out to all vehicle registrants, allotting them a certain amount of ration rights. These checks would then be cashed at Coupon Issuance Points, where the bearer would receive ration coupons to be used at gasoline stations. Large users of gasoline could deposit their allotment checks in accounts at ration banks. Coupons or checks would be freely exchangeable in a white market. A certain percentage of the gasoline supply would be set aside in reserve for use in national emergencies. When the plan was published in the Federal Register, public comments were requested. DOE also solicited comments from private citizens, public interest groups, business and industry, state and local governments. A total of 1126 responses were reveived and these are analyzed in this paper. The second part of the report describes how the comments were classified, and gives a statistical breakdown of the major responses. The last section is a discussion and analysis of theissue raised by commenting agencies, firms, associations, and individuals. (MCW)
Love and rationality: on some possible rational effects of love
Gustavo Ortiz-Millán
2007-01-01
Full Text Available In this paper I defend the idea that rather than disrupting rationality, as the common-sense conception has done it, love may actually help us to develop rational ways of thinking and acting. I make the case for romantic or erotic love, since this is the kind of love that is more frequently associated with irrationality in acting and thinking. I argue that this kind of love may make us develop epistemic and practical forms of rationality. Based on an analysis of its characteristic action tendencies, I argue that love may help us to develop an instrumental form of rationality in determining the best means to achieve the object of love. It may also narrow down the number of practical considerations that may help us to achieve our goals. Finally, love may generate rational ways of belief-formation by framing the parameters taken into account in perception and attention, and by bringing into light only a small portion of the epistemic information available. Love may make us perceive reality more acutely.Neste artigo defendo a idéia de que, em vez de perturbar a racionalidade, como a concepção do senso comum o faz, o amor pode, na verdade, ajudar-nos a desenvolver modos racionais de pensar e agir. Dou bons argumentos para o amor romântico ou erótico, uma vez que esse é o tipo de amor que é mais freqüentemente associado à irracionalidade no agir e no pensar. Argumento que esse tipo de amor pode fazer-nos desenvolver formas epistêmicas e práticas de racionalidade. Com base em uma análise de suas tendências características para a ação, argumento que o amor pode ajudar-nos a desenvolver uma forma instrumental de racionalidade para se determinar o melhor meio de atingir o objeto de amor. Ele também pode limitar o número de considerações práticas que podem ajudar-nos a atingir os nossos objetivos. Finalmente, o amor pode gerar modos racionais de formação de crenças ao estruturar os parâmetros considerados na percepção e na aten
[Rational use of antibiotics].
Walger, P
2016-06-01
International and national campaigns draw attention worldwide to the rational use of the available antibiotics. This has been stimulated by the high prevalence rates of drug-resistant pathogens, such as methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant enterococci (VRE), a threatening spread of development of resistance in Gram-negative rod-shaped bacteria and the selection of Clostridium difficile with a simultaneous clear reduction in the development of new antibiotics. The implementation of antibiotic stewardship programs aims to maintain their effectiveness by a rational use of the available antibiotics. The essential target of therapy with antibiotics is successful treatment of individual patients with bacterial infections. The optimal clinical treatment results can only be achieved when the toxicity, selection of pathogens and development of resistance are minimized. This article presents the principles of a rational antibiotic therapy.
Algebraic Topology, Rational Homotopy
1988-01-01
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moore conjectures on the exponents of the homotopy groups of a finite CW-c-complex and homology of loop spaces. Of particular interest for specialists are papers on construction of the minimal model in tame theory and computation of the Lusternik-Schnirelmann category by means articles on Moore conjectures, on tame homotopy and on the properties of Poincaré series of loop spaces.
Phronesis – hermeneutic rationality
Michał Januszkiewicz
2016-06-01
Full Text Available The paper is an attempt to rethink the problem of rationality in the humanities in the context of hermeneutics. The author argues that this concept of rationality must be founded on the Aristotelian concept of practical reason (phronesis. Phronesis is a need for discernment of the self or rather to find itself in its own, tangible, specific situation. This understanding concerns Being-inthe-world and belongs to what in Martin Heidegger’s ontohermeneutics we can determine precisely as understanding in the hermeneutic sense.
An Educational Interpretation of Jurgen Habermas's Communicative Rationality.
Han, Gicheol
2002-01-01
Suggests taking Habermas's notion of communicative rationality as a reference point from which to organize educational activities and evaluate their "being educational" in the classroom. Communicative rationality in the classroom provides a perspective from which one can establish a normative standard for being educational. (Contains endnotes and…
An Educational Interpretation of Jurgen Habermas's Communicative Rationality.
Han, Gicheol
2002-01-01
Suggests taking Habermas's notion of communicative rationality as a reference point from which to organize educational activities and evaluate their "being educational" in the classroom. Communicative rationality in the classroom provides a perspective from which one can establish a normative standard for being educational. (Contains…
Ideal Theory, Real Rationality
Flyvbjerg, Bent
Understanding rationality and power are key to understanding actual political and administrative behavior. Political and administrative theory that ignores this fact stand in danger of being at best irrelevant or, at worst part of the problem it whishes to solve. The paper presents Jürgen Haberma...
In Between Magic and Rationality, Vibeke Steffen, Steffen Jöhncke, and Kirsten Marie Raahauge bring together a diverse range of ethnographies that examine and explore the forms of reflection, action, and interaction that govern the ways different contemporary societies create and challenge...
Dryden, Windy
2010-01-01
In this title, highly respected author, Windy Dryden, discusses some of the ideas that are central to the theory underpinning rational emotive behaviour therapy (REBT). Founded in 1955 by Albert Ellis (1913-2007) and developed in the intervening years, REBT was the first approach to be created within what is now known as the cognitive behaviour therapy (CBT) tradition.
Diagnosis, Dogmatism, and Rationality.
Rabinowitz, Jonathan; Efron, Noah J.
1997-01-01
Presents findings suggesting that misdiagnoses frequently stem from flaws in human information processing, particularly in collecting and using information. Claims that improved diagnostic tools will not remedy the problem. Drawing on the work of Karl Popper and Robin Collingwood, proposes operational principles to ensure a rational diagnostic…
Ideal Theory, Real Rationality
Flyvbjerg, Bent
Understanding rationality and power are key to understanding actual political and administrative behavior. Political and administrative theory that ignores this fact stand in danger of being at best irrelevant or, at worst part of the problem it whishes to solve. The paper presents Jürgen Habermas...
Rationality and social behavior.
Tullberg, Jan
2003-10-21
This article penetrates the relationship between social behavior and rationality. A critical analysis is made of efforts to classify some behaviors as altruistic, as they simultaneously meet criteria of rationality by not truly being self-destructive. Newcomb's paradox is one attempt to create a hybrid behavior that is both irrational and still meets some criterion of rationality. Such dubious rationality is often seen as a source of altruistic behavior. Group selection is a controversial topic. Sober and Wilson (Unto Others--The Evolution and Psychology of Unselfish Behavior, Harvard University Press, Cambridge, MA, 1998) suggest that a very wide concept of group selection might be used to explain altruism. This concept also includes kin selection and reciprocity, which blurs its focus. The latter mechanisms hardly need further arguments to prove their existence. This article suggests that it is group selection in a strict sense that should be investigated to limit semantic neologism and confusion. In evaluation, the effort to muster a mechanism for altruism out of group selection has not been successful. However, this is not the end to group selection, but rather a good reason to investigate more promising possibilities. There is little reason to burden group selection with the instability of altruism caused by altruistic members of a group having lower fitness than egoistic members. Group selection is much more likely to develop in combination with group egoism. A common project is supported by incitement against free riding, where conformist members joined in solidarity achieve a higher fitness than members pursuing more individualistic options. Group egoism is in no conflict with rationality, and the effects of group selection will be supported rather than threatened by individual selection. Empirical evidence indicates a high level of traits such as conformism and out-group antagonism in line with group egoism. These traits are also likely candidates for
Decision rules and group rationality: cognitive gain or standstill?
Petru Lucian Curşeu
Full Text Available Recent research in group cognition points towards the existence of collective cognitive competencies that transcend individual group members' cognitive competencies. Since rationality is a key cognitive competence for group decision making, and group cognition emerges from the coordination of individual cognition during social interactions, this study tests the extent to which collaborative and consultative decision rules impact the emergence of group rationality. Using a set of decision tasks adapted from the heuristics and biases literature, we evaluate rationality as the extent to which individual choices are aligned with a normative ideal. We further operationalize group rationality as cognitive synergy (the extent to which collective rationality exceeds average or best individual rationality in the group, and we test the effect of collaborative and consultative decision rules in a sample of 176 groups. Our results show that the collaborative decision rule has superior synergic effects as compared to the consultative decision rule. The ninety one groups working in a collaborative fashion made more rational choices (above and beyond the average rationality of their members than the eighty five groups working in a consultative fashion. Moreover, the groups using a collaborative decision rule were closer to the rationality of their best member than groups using consultative decision rules. Nevertheless, on average groups did not outperformed their best member. Therefore, our results reveal how decision rules prescribing interpersonal interactions impact on the emergence of collective cognitive competencies. They also open potential venues for further research on the emergence of collective rationality in human decision-making groups.
When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points
Jezierski, Jerzy
2017-09-01
There are two algebraic lower bounds of the number of n-periodic points of a self-map f:M\\to M of a compact smooth manifold of dimension at least 3 : NF_n(f)=min {#Fix(g^n) ;g\\sim f; g continuous} and NJD_n(f)=min {#Fix}(g^n) ;g\\sim f; g smooth}}. In general NJD_n(f) may be much greater than NF_n(f). We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NF_n(f)=NJD_n(f) holds for all n iff all eigenvalues of a quotient cohomology homomorphism induced by f have moduli \\le 1.
Decision Making: Between Rationality and Reality
Marko Polič
2009-12-01
Full Text Available Almost by definition decision-making is typical human activity, and therefore important psychological subject. The starting point of its classical conception within psychology could be traced back to economy and mathematic, with ideas of human as rational economic being, and conceptualising decision making as choice between two or more alternatives, and as such being a separate event in space and time. Already in fifties Herbert Simon challenged such a view with his concept of bounded rationality, emerging from the joint effect of internal limitations of the human mind, and the structure of external environments in which the mind operates. During the last decades with the shift to the real word situations where decisions are embedded in larger tasks, becoming so part of the study of action, the lost rational human appeared again as efficient creature in the complex environment. Gigerenzer showed how heuristics help in this process.
Hosokawa, Iwao
2007-01-01
A decaying homogeneous isotropic turbulence is treated on the combined bases of the Kolmogorov hypothesis and the cross-independence hypothesis (for a closure of the Monin-Lundgren (ML) hierarchy of many-point velocity distributions) in turbulence. Similarity solutions for one- and two-point velocity distributions are obtained in the viscous, inertial and large-scale ranges of separation distance, from which we can give a reasonable picture of longitudinal and transverse velocity autocorrelation functions for any Reynolds number, even though they are distant from exact solutions of the infinite ML hierarchy. Possibility of non-similarity solutions with other reasonable and more realistic features is unveiled within the same theoretical framework. The cross-independence hypothesis is proved to be inconsistent with the Kolmogorov [1941b. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16-18.] theory in the inertial range. This is the main factor by which our special strategy (described in Introduction) is taken for solving this problem.
Decision rules and group rationality: cognitive gain or standstill?
Curseu, P.L.; Jansen, R.J.G.; Chappin, M.M.H.
2013-01-01
Recent research in group cognition points towards the existence of collective cognitive competencies that transcend individual group members’ cognitive competencies. Since rationality is a key cognitive competence for group decision making, and group cognition emerges from the coordination of indivi
Economic Rationality in the Ultimatum Game
Jan Fiala
2017-03-01
Full Text Available Rigorous application of experimental methodology to the interdisciplinary research of economic decision making is the main purpose of our work. In this paper, we introduce the main decisionmaking theories and outline economic rationality. We explain why we find it useful to discriminate between the “irrational” and “non-rational” components of decision making. We offer an oriented interdisciplinary point of view on economic rationality. In the applied section, we describe the main features of the Ultimatum game and summarize the up-to-date theories explaining the non-rational course of the game. We discuss in detail the reported relations between the nominal value of the stakes and the distribution of the offers and responses. We introduce the blinded, randomized Ultimatum game experiment that we conducted in our laboratory. We stress the importance of anonymity of the study subjects and the difference in salience of a factual reward against a hypothetical reward. We present the results of our study, showing that a duly chosen non-monetary reward, directly inconvertible into money, leads to a different offer distribution in the Ultimatum game without the necessity to invest excessive sums of money in the rewards. We compare our results to research published by other authors. According to our theory, the rational, non-rational and irrational components contribute to the decision making in Ultimatum differently depending on the different reward stakes.
VT - Vermont Rational Service Areas
Vermont Center for Geographic Information — Data Layer Name: Vermont Rational Service Areas (RSAs)Alternate Name: Vermont RSAsOverview:Rational Service Areas (RSAs), originally developed in 2001 and revised in...
Rational management of epilepsy.
Viswanathan, Venkataraman
2014-09-01
Management of epilepsies in children has improved considerably over the last decade, all over the world due to the advances seen in the understanding of the patho-physiology of epileptogenesis, availability of both structural and functional imaging studies along with better quality EEG/video-EEG recordings and the availability of a plethora of newer anti-epileptic drugs which are tailormade to act on specific pathways. In spite of this, there is still a long way to go before one is able to be absolutely rational about which drug to use for which type of epilepsy. There have been a lot of advances in the area of epilepsy surgery and is certainly gaining ground for specific cases. Better understanding of the genetic basis of epilepsies will hopefully lead to a more rational treatment plan in the future. Also, a lot of work needs to be done to dispel various misunderstandings and myths about epilepsy which still exists in our country.
Alternative Disaster Feeding Ration
2012-06-08
is that a healthy person can last about a week without food, but children are more vulnerable lasting for just a few days. In these scenarios, the...ration bar could be edible across different health or dietary constrained populations. For example, diabetics or those with high cholesterol could...Hurricane Katrina was a powerful Category 5 storm that devastated the southeastern states along the Gulf of Mexico in 2005.2 Having seen the aftermath
Realization theory for rational systems
Ně mcová, J.; Schuppen, J.H. van
2008-01-01
In this paper we solve the problem of realization of response maps for rational systems. Sufficient and necessary conditions for a response map to be realizable by a rational system are presented. The properties of rational realizations such as observability, controllability, and minimality are stud
Game interrupted: The rationality of considering the future
Brandon Almy
2013-09-01
Full Text Available The ``problem of points'', introduced by Paccioli in 1494 and solved by Pascal and Fermat 160 years later, inspired the modern concept of probability. Incidentally, the problem also shows that rational decision-making requires the consideration of future events. We show that naive responses to the problem of points are more future oriented and thus more rational in this sense when the problem itself is presented in a future frame instead of the canonical past frame. A simple nudge is sufficient to make decisions more rational. We consider the implications of this finding for hypothesis testing and predictions of replicability.
The rationality of round Interpretation
H. Bastiaanse
2009-01-01
Expanding on a point made by Krifka [6, p.7-8], we show that the fact that a round number has been used significantly increases the posterior probability that that number was intended as an approximation. This increase should typically be enough to make assuming that an approximation was indeed inte
Computational examples of rational string operations on Gorenstein spaces
Naito, Takahito
2015-01-01
In this paper, we give computational examples of string operations over the rational numbers field on Gorenstein spaces introduced by Félix and Thomas. Especially, we determine the structure of rational string operations on the classifying space of a compact connected Lie group and the Borel construction associated to an action of $S^{1}$ to $S^{2}$.
Remo Turchetti
2005-06-01
Full Text Available OBJETIVO: Avaliar o número, forma e topografia dos pontos de vazamento em pacientes com coriorretinopatia serosa central (CRSC. MÉTODOS: Foram avaliados exames de angiografia fluoresceínica realizados utilizando o sistema digital Imagenet e selecionados os casos com diagnóstico de CRSC. Foram excluídos os casos em remissão e os exames referentes a um mesmo episódio. O autor preencheu fichas contendo o número do prontuário, iniciais, sexo, idade, data do exame e características do ponto de vazamento (número, localização e tipo dos casos selecionados. RESULTADOS: Foram incluídos 418 pacientes (455 olhos, com uma relação homem:mulher de 2,32:1, sendo que 91,15% dos pacientes apresentaram a doença unilateralmente e 8,85%, bilateralmente. A idade variou de 19 a 68 anos, com média de 43,04 anos. Dos 455 olhos acometidos, 88,35% apresentaram a forma típica de CRSC, enquanto 10,11% a descompensação do epitélio pigmentário da retina (DEPR e 1,54% com descolamento isolado do epitélio pigmentário da retina (EPR. Entre os casos de CRSC típica, observaram-se 88,81% dos pontos de vazamento em "mancha de tinta" e 11,19% em "chaminé". O quadrante nasal superior foi o mais acometido, abrigando 46,01% dos pontos de vazamento, seguido pelo temporal superior (23,27%, nasal inferior (19,18%, temporal inferior (11,01% e região subfoveal (0,53%. CONCLUSÕES: Na nossa casuística, a CRSC acometeu aproximadamente duas vezes mais homens que mulheres, na maior parte das vezes unilateralmente e em pacientes da 4ª década de vida. Cerca de 90% dos pacientes apresentaram a forma típica da doença, com 1 ou 2 pontos de vazamento em "mancha de tinta". O quadrante nasal superior foi o mais acometido. O descolamento isolado do EPR mostrou-se apresentação rara. Cerca de 10% dos pacientes apresentaram descompensação do EPR.PURPOSE: To evaluate the number, shape and topography of leakage points in patients with central serous chorioretinopathy (CSC
2014-09-26
RD-Ali57 830 ADA (TRADE NAME) COMPILER VALIDATION SUMMARY REPORT: 1/ RATIONAL ENVIRONMENT VERSION R296 FOR RATIONAL Ri888 (U) SOFTECH INC FAIRBORN OH...USoCPY WSSOS.UTM iTS GWAT % : 4 AVF Control Number: AVF-VSR-09.0585 0 IAda Compiler Validation Summary Report: Rational Environment Version A.2.0.6 For...77. . 77-4- .- REPORT DOCUMENTATION PAGERED1S1IT0$ L~~~~ 1YP 0061 1tO REPORT 6 PL eDD COVERED Ada* Compiler Validation Summary Report: Rational May
Rational choices for the wavelengths of a two color interferometer
Jobes, F.C.
1995-07-01
If in a two color interferometer for plasma density measurements, the two wavelengths are chosen to have a ratio that is a rational number, and if the signals from each of the wavelengths are multiplied in frequency by the appropriate integer of the rational number and then heterodyned together, the resultant signal will have all effects of component motion nulled out. A phase measurement of this signal will have only plasma density information in it. With CO{sub 2} lasers, it is possible to find suitable wavelength pairs which are close enough to rational numbers to produce an improvement of about 100 in density resolution, compared to standard two color interferometers.
Shiomi, Kozue; Sato, Katsufumi; Ponganis, Paul J
2012-01-01
At some point in a dive, breath-hold divers must decide to return to the surface to breathe. The issue of when to end a dive has been discussed intensively in terms of foraging ecology and behavioral physiology, using dive duration as a temporal parameter. Inevitably, however, a time lag exists between the decision of animals to start returning to the surface and the end of the dive, especially in deep dives. In the present study, we examined the decision time in emperor penguins under two different conditions: during foraging trips at sea and during dives at an artificial isolated dive hole. It was found that there was an upper limit for the decision-to-return time irrespective of dive depth in birds diving at sea. However, in a large proportion of dives at the isolated dive hole, the decision-to-return time exceeded the upper limit at sea. This difference between the decision times in dives at sea versus the isolated dive hole was accounted for by a difference in stroke rate. The stroke rates were much lower in dives at the isolated hole and were inversely correlated with the upper limit of decision times in individual birds. Unlike the decision time to start returning, the cumulative number of strokes at the decision time fell within a similar range in the two experiments. This finding suggests that the number of strokes, but not elapsed time, constrained the decision of emperor penguins to return to the surface. While the decision to return and to end a dive may be determined by a variety of ecological, behavioral and physiological factors, the upper limit to that decision time may be related to cumulative muscle workload.
Tarnopolski, Mariusz
2016-11-01
The long range dependence of the fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst exponent H. Considering the realizations of these three processes as time series, they might be described by their statistical features, such as half of the ratio of the mean square successive difference to the variance, A, and the number of turning points, T. This paper investigates the relationships between A and H, and between T and H. It is found numerically that the formulae A(H) = aebH in case of fBm, and A(H) = a + bHc for fGn and DfGn, describe well the A(H) relationship. When T(H) is considered, no simple formula is found, and it is empirically found that among polynomials, the fourth and second order description applies best. The most relevant finding is that when plotted in the space of (A , T) , the three process types form separate branches. Hence, it is examined whether A and T may serve as Hurst exponent indicators. Some real world data (stock market indices, sunspot numbers, chaotic time series) are analyzed for this purpose, and it is found that the H's estimated using the H(A) relations (expressed as inverted A(H) functions) are consistent with the H's extracted with the well known wavelet approach. This allows to efficiently estimate the Hurst exponent based on fast and easy to compute A and T, given that the process type: fBm, fGn or DfGn, is correctly classified beforehand. Finally, it is suggested that the A(H) relation for fGn and DfGn might be an exact (shifted) 3 / 2 power-law.
Rational and moral action : a critical survey of rational choice theory
de Jonge, J.P.R.
2009-01-01
This book is about rational choice theory from a different point of view. It is different for three reasons. First, it pays attention to the unintended consequences of intended actions. Second, it employs a non-instrumental approach to moral actions. And third, it argues that choice opportunities ma
Rational and moral action : a critical survey of rational choice theory
de Jonge, J.P.R.
2009-01-01
This book is about rational choice theory from a different point of view. It is different for three reasons. First, it pays attention to the unintended consequences of intended actions. Second, it employs a non-instrumental approach to moral actions. And third, it argues that choice opportunities ma
Mocanu, L. M.; Crawford, T. M.; Benson, B. A.; Bleem, L. E.; Carlstrom, J. E.; Chang, C. L.; Crites, A. T. [Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637 (United States); Vieira, J. D. [California Institute of Technology, Pasadena, CA 91125 (United States); Aird, K. A. [University of Chicago, Chicago, IL 60637 (United States); Aravena, M. [European Southern Observatory, Alonso de Córdova 3107, Vitacura Santiago (Chile); Austermann, J. E.; Everett, W. B.; Halverson, N. W. [Department of Astrophysical and Planetary Sciences and Department of Physics, University of Colorado, Boulder, CO 80309 (United States); Béthermin, M. [Laboratoire AIM-Paris-Saclay, CEA/DSM/Irfu-CNRS-Université Paris Diderot, CEA-Saclay, Orme des Merisiers, F-91191 Gif-sur-Yvette (France); Bothwell, M. [Cavendish Laboratory, University of Cambridge, 19 J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Chapman, S. [Department of Physics and Atmospheric Science, Dalhousie University, Halifax NS B3H 3J5 (Canada); Cho, H.-M. [NIST Quantum Devices Group, Boulder, CO 80305 (United States); De Haan, T.; Dobbs, M. A. [Department of Physics, McGill University, Montreal, Quebec H3A 2T8 (Canada); George, E. M., E-mail: lmocanu@uchicago.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); and others
2013-12-10
We present a point-source catalog from 771 deg{sup 2} of the South Pole Telescope Sunyaev-Zel'dovich survey at 95, 150, and 220 GHz. We detect 1545 sources above 4.5σ significance in at least one band. Based on their relative brightness between survey bands, we classify the sources into two populations, one dominated by synchrotron emission from active galactic nuclei, and one dominated by thermal emission from dust-enshrouded star-forming galaxies. We find 1238 synchrotron and 307 dusty sources. We cross-match all sources against external catalogs and find 189 unidentified synchrotron sources and 189 unidentified dusty sources. The dusty sources without counterparts are good candidates for high-redshift, strongly lensed submillimeter galaxies. We derive number counts for each population from 1 Jy down to roughly 11, 4, and 11 mJy at 95, 150, and 220 GHz. We compare these counts with galaxy population models and find that none of the models we consider for either population provide a good fit to the measured counts in all three bands. The disparities imply that these measurements will be an important input to the next generation of millimeter-wave extragalactic source population models.
Kurudirek, Murat; Aygun, Murat; Erzeneoğlu, Salih Zeki
2010-06-01
The trommel sieve waste (TSW) which forms during the boron ore production is considered to be a promising building material with its use as an admixture with Portland cement and is considered to be an alternative radiation shielding material, also. Thus, having knowledge on the chemical composition and radiation interaction properties of TSW as compared to other building materials is of importance. In the present study, chemical compositions of the materials used have been determined using a wavelength dispersive X-ray fluorescence spectrometer (WDXRFS). Also, TSW, some commonly used building materials (Portland cement, lime and pointing) and their admixtures with TSW have been investigated in terms of total mass attenuation coefficients (mu/rho), photon interaction cross sections (sigma(t)), effective atomic numbers (Z(eff)) and effective electron densities (N(e)) by using X-rays at 22.1, 25keV and gamma-rays at 88keV photon energies. Possible conclusions were drawn with respect to the variations in photon energy and chemical composition.
Schott, Hans
2003-04-01
The following linear equation correlates the cloud point (CP) of water-soluble polyoxyethylated nonionic surfactants (NSs) with the average number p of oxyethylene units per molecule: (p - p0)/CP = a + b(p - p0). Here p0 is the smallest value of p that confers solubility in cold water: In a homologous series of NSs, it belongs to the surfactant with CP = 0 degrees C. Plots of CP versus p for five representative homologous series of NSs consist of three segments: A steeply ascending, nearly straight line, a transition region that ranges from p = 15-22 to p = 20-28, and a nearly horizontal plateau that approaches asymptotically the CPs of polyethylene glycols with molecular weights between 30,000 and 4400. These CPs range from 113 to 130 degrees C. Most CPs for NSs were taken from the literature or measured on commercially available samples; eight CPs above 100 degrees C were measured on newly synthesized surfactants. Previously published linear equations correlating CP with p cover only NSs with p or = 100. It can be used for selecting specific NSs for high-temperature applications. The hydrophile-lipophile balance of the surfactant with p = p0 oxyethylene units, namely, HLB0, is a novel quantitative measure of the hydrophobicity of the hydrocarbon moiety of the relevant homologous NS series. Its value reflects the size, composition, and structure of the hydrocarbon moiety.
Tarnopolski, Mariusz
2015-01-01
The long range dependence of the fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst exponent $H$ (HE). Considering these three processes in terms of time series, they might be described by their statistical features, such as half of the ratio of the mean square successive difference to the variance, $\\mathcal{A}$, and the number of turning points, $T$. This paper investigates the correlations between $\\mathcal{A}$ and $T$ on $H$. It is found that the formulas $\\mathcal{A}=a{\\rm e}^{bH}$ in case of fBm, and $\\mathcal{A}=a+bH^c$ for fGn and DfGn, describe the $\\mathcal{A}(H)$ relationship. When $T(H)$ is considered, no simple formula is found, and it is empirically found that among polynomials, the fourth and second order description applies. When plotted in the space of $(\\mathcal{A},T)$, the three process types form separated branches. Hence, it is examined whether $\\mathcal{A}$ and $T$ may serve as HE indicators. Some real world data are...
Yoshida, Yutaka; Yokoyama, Kiyoko; Ishii, Naohiro
It is reported that frequency component of approximately 0.25Hz of heart rate time series (RSA) is corresponding to the respiratory frequency. In this paper, we proposed that continuous estimation method of respiratory fequency during sleep using the number of extreme points of heart rate time series in real time. Equation for calculation of the method is very simple and the method can continuously calculate frequency by window width of about 18 beats. To evaluate accuracy of proposal method, RSA frequency was calculated using proposal method from the heart rate time series during supine rest. Result, minimum error rate was observed when RSA had time lag for about 11s and error rate was about 13.8%. Result of estimating RSA frequency time series during sleep, it varied regularly during non-REM and varied irregularly during REM. This result is similar as report of previous study about respiratory variability during sleep. Therefore, it is considered that proposal method possible to apply respiratory monitoring system during sleep.
Privacy-Enhancing Auctions Using Rational Cryptography
Miltersen, Peter Bro; Nielsen, Jesper Buus; Triandopoulos, Nikolaos
2009-01-01
We consider enhancing with privacy concerns a large class of auctions, which include sealed-bid single-item auctions but also general multi-item multi-winner auctions, our assumption being that bidders primarily care about monetary payoff and secondarily worry about exposing information about...... show how to use rational cryptography to approximately implement any given ex interim individually strictly rational equilibrium of such an auction without a trusted mediator through a cryptographic protocol that uses only point-to-point authenticated channels between the players. By “ex interim...... close to the original equilibrium.Supported by the Center for Algorithmic Game Theory, funded by The Carlsberg Foundation....
NEVILLE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS
陈之兵; 顾传青; 徐晨
2004-01-01
A new kind of vector valued rational interpolants is established by means of Samelson inverse, with scalar numerator and vector valued denominator. It is essen tially different from that of Graves-Morris(1983), where the interpolants are constructed by Thiele-type continued fractions with vector valued numerator and scalar denominator. The new approach is more suitable to calculate the value of a vector valued function for a given point. And an error formula is also given and proven.
Mandal, Soma; Moudgil, Mee'nal; Mandal, Sanat K
2009-12-25
In this article, current knowledge of drug design is reviewed and an approach of rational drug design is presented. The process of drug development is challenging, expensive, and time consuming, although this process has been accelerated due to the development of computational tools and methodologies. The current target based drug design approach is incomplete because most of the drugs developed by structure guided approaches have been shown to have serious toxic side effects. Otherwise these drugs would have been an ideal choice for the treatment of diseases. Hence, rational drug design would require a multidisciplinary approach. In this regard, incorporation of gene expression technology and bioinformatics tools would be indispensable in the structure based drug design. Global gene expression data and analysis of such data using bioinformatics tools will have numerous benefits such as efficiency, cost effectiveness, time saving, and will provide strategies for combination therapy in addition to overcoming toxic side effects. As a result of incorporation of gene expression data, partial benefit of the structure based drug design is slowly emerging and rapidly changing the approach of the drug development process. To achieve the full benefit of developing a successful drug, multidisciplinary approaches (approaches such as computational chemistry and gene expression analysis, as discussed in this article) would be necessary. In the future, there is adequate room for the development of more sophisticated methodologies.
Schwerdt, R
2005-08-01
The intraprofessional discourse about economical aspects in nursing from an ethical point of view has not taken place yet. To cope with the increasing restriction of resources, some preconditions have to be met: It is necessary to communicate issues in rationalizing and rationing in nursing openly. Person-oriented criteria in the nursing process indicate a high level of competence and user-oriented quality in nursing care. But nursing professionals do not decide in favor or against resources to perform this task on a high or poor quality level. Democratic decision-making on providing nursing services depends on a continuous societal discourse about allocation criteria.
Analysis of Price Stackelberg Duopoly Game with Bounded Rationality
Lian Shi
2014-01-01
Full Text Available The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.
Combinatorial Constructions for Sifting Primes and Enumerating the Rationals
Gnang, Edinah K
2012-01-01
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that such mappings achieve much more than enumeration of rooted trees. We discuss two related structural bijections. The first corresponds to a bijective map between integers and rooted trees. The first bijection also suggests a new algorithm for sifting primes. The second bijection extends the first one in order to map rational numbers to a family of rooted trees. The second bijection suggests a new combinatorial construction for generating reduced rational numbers, thereby producing refinements of the output of the Wilf-Calkin[1] Algorithm.
Credit rationing and firm size
G. CALCAGNINI
2013-10-01
Full Text Available This paper examines the likelihood of credit rationing faced by firms of different size. Contrary to common thought, several recent contributions on this topic argue that, when rationing credit, size alone is not a sufficient condition for discriminating between firms. We show that this result can be predicted using a framework based on the Stiglitz-Weiss model. In particular, in an environment of asymmetric information, we highlight how the likelihood of credit rationing depends upon the shape of the distribution function of project returns, especially its asymmetry and Kurtosis. Our empirical results do not support the hypothesis that small firms face more credit rationing than larger firms.
Hegel's phenomenology of rationality
Huggler, Jørgen
2009-01-01
The aim of this chapter is to elucidate Hegel's conception of rationality in the Phänomenologie des Geistes (1807), and to defend the thesis that he is an author engaged in discussion with a wide variety of sources. He uses sceptical reasoning to form a line of argument with a necessary progression......, although the various materials that he considers are not linked in a simple, compelling logical way. The paper discusses what Hegel aimed at and the methods he used to reach his goal (sect. 1). These considerations are then used to cast an eye on the development of the contents of the book (sect. 2). Last......, the paper presents a metaphysical interpretation of the course of experiences and discusses why Hegel's sceptical method is adequate to the metaphysics of spirit with which the book concludes (sect. 3)....
Rational top and its classical r-matrix
Aminov, G.; Arthamonov, S.; Smirnov, A.; Zotov, A.
2014-08-01
We construct a rational integrable system (the rational top) on a co-adjoint orbit of SL N Lie group. It is described by the Lax operator with spectral parameter and classical non-dynamical skew-symmetric r-matrix. In the case of the orbit of minimal dimension the model is gauge equivalent to the rational Calogero-Moser (CM) system. To obtain the results we represent the Lax operator of the CM model in two different factorized forms—without spectral parameter (related to the spinless case) and another one with the spectral parameter. The latter gives rise to the rational top while the first one is related to generalized Cremmer-Gervais r-matrices. The gauge transformation relating the rational top and CM model provides the classical rational version of the IRF-Vertex correspondence. From the geometrical point of view it describes the modification of SL(N,{C})-bundles over degenerated elliptic curve. In view of the Symplectic Hecke Correspondence the rational top is related to the rational spin CM model. Possible applications and generalizations of the suggested construction are discussed. In particular, the obtained r-matrix defines a class of KZB equations.
Rational Top and its Classical R-matrix
Aminov, G; Smirnov, A; Zotov, A
2014-01-01
We construct a rational integrable system (the rational top) on a coadjoint orbit of ${\\rm SL}_N$ Lie group. It is described by the Lax operator with spectral parameter and classical non-dynamical skew-symmetric $r$-matrix. In the case of the orbit of minimal dimension the model is gauge equivalent to the rational Calogero-Moser (CM) system. To obtain the results we represent the Lax operator of the CM model in two different factorized forms -- without spectral parameter (related to spinless case) and another one with the spectral parameter. The later gives rise to the rational top while the first one is related to generalized Cremmer-Gervais $r$-matrices. The gauge transformation relating the rational top and CM model provides a classical rational version of the IRF-Vertex correspondence. From a geometrical point of view it describes the modification of ${\\rm SL}(N,\\mathbb C)$-bundles over degenerated elliptic curve. In view of Symplectic Hecke Correspondence the rational top is related to the rational spin ...
Source localization using rational approximation on plane sections
Clerc, M.; Leblond, J.; Marmorat, J.-P.; Papadopoulo, T.
2012-05-01
In functional neuroimaging, a crucial problem is to localize active sources within the brain non-invasively, from knowledge of electromagnetic measurements outside the head. Identification of point sources from boundary measurements is an ill-posed inverse problem. In the case of electroencephalography (EEG), measurements are only available at electrode positions, the number of sources is not known in advance and the medium within the head is inhomogeneous. This paper presents a new method for EEG source localization, based on rational approximation techniques in the complex plane. The method is used in the context of a nested sphere head model, in combination with a cortical mapping procedure. Results on simulated data prove the applicability of the method in the context of realistic measurement configurations.
Fabac, Robert; Radošević, Danijel; Magdalenić, Ivan
2014-01-01
When considering strategic games from the conceptual perspective that focuses on the questions of participants' decision-making rationality, the very issues of modelling and simulation are rarely discussed. The well-known Rational Pigs matrix game has been relatively intensively analyzed in terms of reassessment of the logic of two players involved in asymmetric situations as gluttons that differ significantly by their attributes. This paper presents a successful attempt of using autogenerator for creating the framework of the game, including the predefined scenarios and corresponding payoffs. Autogenerator offers flexibility concerning the specification of game parameters, which consist of variations in the number of simultaneous players and their features and game objects and their attributes as well as some general game characteristics. In the proposed approach the model of autogenerator was upgraded so as to enable program specification updates. For the purpose of treatment of more complex strategic scenarios, we created the Rational Pigs Game Extended (RPGE), in which the introduction of a third glutton entails significant structural changes. In addition, due to the existence of particular attributes of the new player, "the tramp," one equilibrium point from the original game is destabilized which has an influence on the decision-making of rational players.
BIVARIATE LAGRANGE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS
Chuan-qing Gu; Gong-qing Zhu
2002-01-01
An axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points is at first presented in this paper. A two-variable vector valued rational interpolation formula is explicitly constructed in the following form: the determinantal formulas for denominator scalar polynomials and for numerator vector polynomials,which possess Lagrange-type basic function expressions. A practical criterion of existence and uniqueness for interpolation is obtained. In contrast to the underlying method, the method of bivariate Thiele-type vector valued rational interpolation is reviewed.
On the Rational Polytopes with Chvatal Rank 1
2016-11-30
On the Rational Polytopes with Chvátal Rank 1 Gérard Cornuéjols∗ Dabeen Lee† Yanjun Li‡ November 30, 2016 Abstract In this paper, we study the...Chvátal rank 1 seems hard to verify though. We prove that deciding emptiness of the Chvátal closure of a given rational polytope P is NP-complete, even...when P is contained in the unit hypercube or is a rational simplex, and even when P does not contain any integer point. This has two implications: (i
DRGs: justice and the invisible rationing of health care resources.
Fleck, L M
1987-05-01
Are DRGs just? This is the primary question which this essay will answer. But there is a prior methodological question that also needs to be addressed: How do we go about rationally (non-arbitrarily) assessing whether DRGs are just or not? I would suggest that grand, ideal theories of justice (Rawls, Nozick) have only very limited utility for answering this question. What we really need is a theory of "interstitial justice," that is, an approach to making justice judgments that is suitable to assessing the social practices and institutions that comprise the interstices of our social life as opposed to its basic structure. Rawls's appeal to "our considered moral judgments" provides us with a useful starting point for this task, which we shall discuss in the first part of this essay. In the second part, we shall actually assess DRGs from the perspective of interstitial justice. What we shall show is that DRGs violate a large number of our considered judgments regarding a just approach to financing health care for the elderly in a cost-effective manner. This is true to such an extent that efforts to reform DRGs and make them fairer, such as the recent effort by Robert Veatch, should be abandoned. In the concluding section of the essay we discuss one especially pernicious feature of DRGs, namely, that they represent an invisible approach to rationing access to health care. In the minds of many this is one of the virtues of DRGs. That claim needs critical examination.
Adaptive Rationality, Adaptive Behavior and Institutions
Volchik Vyacheslav, V.
2015-12-01
Full Text Available The economic literature focused on understanding decision-making and choice processes reveals a vast collection of approaches to human rationality. Theorists’ attention has moved from absolutely rational, utility-maximizing individuals to boundedly rational and adaptive ones. A number of economists have criticized the concepts of adaptive rationality and adaptive behavior. One of the recent trends in the economic literature is to consider humans irrational. This paper offers an approach which examines adaptive behavior in the context of existing institutions and constantly changing institutional environment. It is assumed that adaptive behavior is a process of evolutionary adjustment to fundamental uncertainty. We emphasize the importance of actors’ engagement in trial and error learning, since if they are involved in this process, they obtain experience and are able to adapt to existing and new institutions. The paper aims at identifying relevant institutions, adaptive mechanisms, informal working rules and practices that influence actors’ behavior in the field of Higher Education in Russia (Rostov Region education services market has been taken as an example. The paper emphasizes the application of qualitative interpretative methods (interviews and discourse analysis in examining actors’ behavior.
Rational Convolution Roots of Isobaric Polynomials
Conci, Aura; Li, Huilan; MacHenry, Trueman
2014-01-01
In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of determinants and permanents, respectively. The underlying root formulas for GFPs and for weighted isobaric polynomials (WIPs), which appeared in an earlier paper by MacHenry and Tudose, make use of two types of operators. These operators are derived from the generating functions for Stirling numbers of the first kind and second kind. Hen...
Maria José Ferreira da Silva
2008-12-01
Full Text Available We present a reflection regarding operations with fractional numbers focusing on the part-all conception through some activities that can contribute to teaching practices at the elementary school level. A brief characterization of the all-part conception is provided along with descriptions of activities involving the four basic operations based on the use of flat figures, although other conceptions may emerge during the solution. We limit our considerations to this conception because it is the most frequent, in textbooks as well as teacher practice, although it is not used to justify operational rules of fractional numbers. Key-words: Fractions. Fractional Numbers. Operations.Neste artigo, apresentamos uma reflexão a respeito das operações com números fracionários focalizando a concepção parte-todo por meio de algumas atividades que possam contribuir para a prática docente na escola básica. O estudo explicita uma breve caracterização da concepção parte-todo e atividades envolvendo as quatro operações fundamentais tratadas em figuras planas, embora outras concepções possam ser mobilizadas durante a solução. Restringimos nossas considerações a essa concepção visto ser a mais freqüente, tanto em livros didáticos, quanto na prática do professor, embora não seja utilizada para justificar as regras operatórias dos números fracionários. Palavras-chave: Frações. Números Fracionários. Operações.
Rational formality of mapping spaces
Felix, Yves
2010-01-01
Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the rational homotopy type of a finite product of odd dimensional spheres.
Rationality problem for algebraic tori
Hoshi, Akinari
2017-01-01
The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for G-...
Rational noncompliance with prescribed medical treatment.
Stewart, Douglas O; DeMarco, Joseph P
2010-09-01
Despite the attention that patient noncompliance has received from medical researchers, patient noncompliance remains poorly understood and difficult to alter. With a better theory of patient noncompliance, both greater success in achieving compliance and greater respect for patient decision making are likely. The theory presented, which uses a microeconomic approach, bridges a gap in the extant literature that has so far ignored the contributions of this classic perspective on decision making involving the tradeoff of costs and benefits. The model also generates a surprising conclusion: that patients are typically acting rationally when they refuse to comply with certain treatments. However, compliance is predicted to rise with increased benefits and reduced costs. The prediction that noncompliance is rational is especially true in chronic conditions at the point that treatment begins to move closer to the medically ideal treatment level. Although the details of this theory have not been tested empirically, it is well supported by existing prospective and retrospective studies.
Towards a formal logic of design rationalization
Galle, Per
1997-01-01
Certain extensions to standard predicate logic are proposed and used as a framework for critical logical study of patterns of inference in design reasoning. It is shown that within this framework a modal logic of design rationalization (suggested by an empirical study reported earlier) can...... be formally defined in terms of quantification over a universe of discourse of ‘relevant points of view’. Five basic principles of the extended predicate logic are listed, on the basis of which the validity of ten modal patterns of inference encountered in design rationalization is tested. The basic idea...... of reducing modality to quantification is traced back to the philosophy of von Wright, and the approach is compared to that of related work on logic in design....
Quantum contextuality for rational vectors
Cabello, Adan
2010-01-01
The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D. A. Meyer, Phys. Rev. Lett. 83, 3751 (1999)] that the inconsistency would disappear when we are restricted to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A. A. Klyachko et al., Phys. Rev. Lett. 101, 020403 (2008)] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.
Quantum contextuality for rational vectors
Cabello, Adan, E-mail: adan@us.e [Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain); Larsson, Jan-Ake, E-mail: jan-ake.larsson@liu.s [Institutionen foer Systemteknik, Linkoepings Universitet, SE-581 83 Linkoeping (Sweden)
2010-12-01
The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D.A. Meyer, Phys. Rev. Lett. 83 (1999) 3751] that the inconsistency would disappear when restricting to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A.A. Klyachko et al., Phys. Rev. Lett. 101 (2008) 020403] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.
Limited rationality and strategic interaction
Fehr, Ernst; Tyran, Jean-Robert
2008-01-01
Much evidence suggests that people are heterogeneous with regard to their abilities to make rational, forward-looking decisions. This raises the question as to when the rational types are decisive for aggregate outcomes and when the boundedly rational types shape aggregate results. We examine...... this question in the context of a long-standing and important economic problem: the adjustment of nominal prices after an anticipated monetary shock. Our experiments suggest that two types of bounded rationality-money illusion and anchoring-are important behavioral forces behind nominal inertia. However......, depending on the strategic environment, bounded rationality has vastly different effects on aggregate price adjustment. If agents' actions are strategic substitutes, adjustment to the new equilibrium is extremely quick, whereas under strategic complementarity, adjustment is both very slow and associated...
Standby gasoline rationing plan: narrative
1979-02-01
The objectives of the rationing plan are to provide a mechanism capable of maintaining an orderly and equitable market for gasoline in a severe supply shortfall, and capable of rapid implementation; and to comply with requirements of EPCA, which mandates the development of a contingency rationing plan. Eligibility for ration allotments will be based principally on motor vehicle registration records, maintained in a national vehicle registration file. Supplemental allotments will be granted for certain priority activities to ensure the maintenance of essential public services. Supplemental allotments will also be granted to businesses and government organizations with significant off-highway gasoline requirements. Local rationing boards or other offices will be established by states, to provide special allotments to hardship applicants, within DOE guidelines. The background and history of the plan are described. The gasoline rationing plan operations, government operations, program costs, staffing, and funding are also detailed in this report. (MCW)
Rationality in a general model of choice
Somdeb Lahiri
2015-09-01
Full Text Available In this paper we consider choice correspondences which may be empty-valued. We study conditions under which such choice correspondences are rational, transitively rational, partially rational, partially almost transitive rational, partially almost quasi-transitive rational. This provides fresh impetus and understanding of multi-criteria decision making.
WANG JiaMin
2009-01-01
In this paper we consider a retail service facility with cross-trained workers who can perform operations in both the front room and back room. Workers are brought from the back room to the front room and vice versa depending on the number of customers in the system. A loss of productivity occurs when a worker returns to the back room. Two problems are studied. In the first problem, given the number of workers available, we determine an optimal deterministic switching policy so that the expected number of customers in queue is minimized subject to a constraint ensuring that there is a sufficient workforce to fulfill the functions in the back room. In the second problem, the number of workers needed is minimized subject to an additional constraint requiring that the expected number of customers waiting in queue is bounded above by a given threshold value. Exact solution procedures are developed and illustrative numerical examples are presented.
Brothers, Kyle B
2011-04-01
Provider claims to conscientious objection have generated a great deal of heated debate in recent years. However, the conflicts that arise when providers make claims to the "conscience" are only a subset of the more fundamental challenges that arise in health care practice when patients and providers come into conflict. In this piece, the author provides an account of patient-provider conflict from within the moral tradition of St. Thomas Aquinas. He argues that the practice of health care providers should be understood as a form of practical reasoning and that this practical reasoning must necessarily incorporate both "moral" and "professional" commitments. In order to understand how the practical reasoning of provider should account for the needs and commitments of the patient and vice versa, he explores the account of dependence provided by Alasdair MacIntyre in his book Dependent Rational Animals. MacIntyre argues that St. Thomas' account of practical reasoning should be extended and adapted to account for the embodied vulnerability of all humans. In light of this insight, providers must view patients not only as the subjects of their moral reflection but also as fellow humans upon whom the provider depends for feedback on the effectiveness and relevance of her practical reasoning. The author argues that this account precludes responsive providers from adopting either moral or professional conclusions on the appropriateness of interventions outside the individual circumstances that arise in particular situations. The adoption of this orientation toward patients will neither eradicate provider-patient conflict nor compel providers to perform interventions to which they object. But this account does require that providers attend meaningfully to the suffering of patients and seek feedback on whether their intervention has effectively addressed that suffering.
Scalable Mechanisms for Rational Secret Sharing
Dani, Varsha; Saia, Jared
2012-01-01
We consider the classical secret sharing problem in the case where all agents are selfish but rational. In recent work, Kol and Naor show that, when there are two players, in the non-simultaneous communication model, i.e. when rushing is possible, there is no Nash equilibrium that ensures both players learn the secret. However, they describe a mechanism for this problem, for any number of players, that is an epsilon-Nash equilibrium, in that no player can gain more than epsilon utility by deviating from it. Unfortunately, the Kol and Naor mechanism, and, to the best of our knowledge, all previous mechanisms for this problem require each agent to send O(n) messages in expectation, where n is the number of agents. This may be problematic for some applications of rational secret sharing such as secure multi-party computation and simulation of a mediator. We address this issue by describing mechanisms for rational secret sharing that are designed for large n. Both of our results hold for n > 2, and are Nash equil...
Zinke, Stephan
2017-02-01
Memory sensitive applications for remote sensing data require memory-optimized data types in remote sensing products. Hierarchical Data Format version 5 (HDF5) offers user defined floating point numbers and integers and the n-bit filter to create data types optimized for memory consumption. The European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) applies a compaction scheme to the disseminated products of the Day and Night Band (DNB) data of Suomi National Polar-orbiting Partnership (S-NPP) satellite's instrument Visible Infrared Imager Radiometer Suite (VIIRS) through the EUMETSAT Advanced Retransmission Service, converting the original 32 bits floating point numbers to user defined floating point numbers in combination with the n-bit filter for the radiance dataset of the product. The radiance dataset requires a floating point representation due to the high dynamic range of the DNB. A compression factor of 1.96 is reached by using an automatically determined exponent size and an 8 bits trailing significand and thus reducing the bandwidth requirements for dissemination. It is shown how the parameters needed for user defined floating point numbers are derived or determined automatically based on the data present in a product.
Vaccines: from empirical development to rational design.
Christine Rueckert
Full Text Available Infectious diseases are responsible for an overwhelming number of deaths worldwide and their clinical management is often hampered by the emergence of multi-drug-resistant strains. Therefore, prevention through vaccination currently represents the best course of action to combat them. However, immune escape and evasion by pathogens often render vaccine development difficult. Furthermore, most currently available vaccines were empirically designed. In this review, we discuss why rational design of vaccines is not only desirable but also necessary. We introduce recent developments towards specifically tailored antigens, adjuvants, and delivery systems, and discuss the methodological gaps and lack of knowledge still hampering true rational vaccine design. Finally, we address the potential and limitations of different strategies and technologies for advancing vaccine development.
NOTES FOR THE CONSTRUCTION OF ENVIRONMENTAL RATIONALITY
Munir Jorge Felício
2015-12-01
Full Text Available The notes for the construction of Environmental Rationality proposed in this text were gathered from a contribution of an analysis of phenomenology, epistemology, and ontology relating to Marx. This initiative aims to broaden and deepen the understanding of environmental issues whose global changes raise challenges, especially for the scientific community. It is to question the development of the economic rationality from the degradation of natural resources engendered by the current socio-economic development model. This model is based on the increase of productivity, technological expansion and maintains the norm as if natural resources were still considered abundant and limitless. The transition of this Environmental Rationality is a development sought by using the knowledge gained from the analysis possibilities of phenomenology. Among these possibilities, the indicated interdisciplinary schools of thought, as required by epistemology, can become an interesting research strategy, since it has as the starting point the external demands, where the elements of the current environmental issue exist, and its consequences.
Rational drug therapy education in clinical phase carried out by task-based learning.
Bilge, S Sırrı; Akyüz, Bahar; Ağrı, Arzu Erdal; Özlem, Mıdık
2017-01-01
Irrational drug use results in drug interactions, treatment noncompliance, and drug resistance. Rational pharmacotherapy education is being implemented in many faculties of medicine. Our aim is to introduce rational pharmacotherapy education by clinicians and to evaluate task-based rational drug therapy education in the clinical context. The Kirkpatrick's evaluation model was used for the evaluation of the program. The participants evaluated the program in terms of constituents of the program, utilization, and contribution to learning. Voluntary participants responded to the evaluation forms after the educational program. Data are evaluated using both quantitative and qualitative tools. SPSS (version 21) used for quantitative data for determining mean and standard deviation values. Descriptive qualitative analysis approach is used for the analysis of open-ended questions. It was revealed that the program and its components have been favorable. A total 95.9% of the students consider the education to be beneficial. Simulated patients practice and personal drug choice/problem-based learning sessions were appreciated by the students in particular. 93.9% of the students stated that all students of medicine should undergo this educational program. Among the five presentations contained in the program, "The Principles of Prescribing" received the highest points (9 ± 1.00) from participating students in general evaluation of the educational program. This study was carried out to improve task-based rational drug therapy education. According to feedback from the students concerning content, method, resource, assessment, and program design; some important changes, especially in number of facilitators and indications, are made in rational pharmacotherapy education in clinical task-based learning program.
Calculation of Complexity Costs – An Approach for Rationalizing a Product Program
Hansen, Christian Lindschou; Mortensen, Niels Henrik; Hvam, Lars
2012-01-01
This paper proposes an operational method for rationalizing a product program based on the calculation of complexity costs. The method takes its starting point in the calculation of complexity costs on a product program level. This is done throughout the value chain ranging from component...... inventories at the factory sites, all the way to the distribution of finished goods from distribution centers to the customers. The method proposes a step-wise approach including the analysis, quantification and allocation of product program complexity costs by the means of identifying of a number...
Riedl, Dennis; Heuer, Andreas; Strauss, Bernd
2015-06-01
Incentives guide human behavior by altering the level of external motivation. We apply the idea of loss aversion from prospect theory (Kahneman & Tversky, 1979) to the point reward systems in soccer and investigate the controversial impact of the three-point rule on reducing the fraction of draws in this sport. Making use of the Poisson nature of goal scoring, we compared empirical results with theoretically deduced draw ratios from 24 countries encompassing 20 seasons each (N = 118.148 matches). The rule change yielded a slight reduction in the ratio of draws, but despite adverse incentives, still 18% more matches ended drawn than expected, t(23) = 11.04, p < .001, d = 2.25, consistent with prospect theory assertions. Alternative point systems that manipulated incentives for losses yielded reductions at or below statistical expectation. This provides support for the deduced concept of how arbitrary aims, such as the reduction of draws in the world's soccer leagues, could be more effectively accomplished than currently attempted.
Collective action and rationality models
Luis Miguel Miller Moya
2004-01-01
Full Text Available The Olsonian theory of collective action (Olson, 1965 assumes a model of economic rationality, based on a simple calculus between costs and benefits, that can be hardly hold at present, given the models of rationality proposed recently by several fields of research. In relation to these fields, I will concentrate in two specific proposals, namely: evolutionary game theory and, over all, the theory of bounded rationality. Both alternatives are specially fruitful in order to propose models that do not need a maximizing rationality, or environments of complete and perfect information. Their approaches, based on the possibility of individual learning over the time, have contributed to the analysis of the emergence of social norms, which is something really necessary to the resolution of problems related to cooperation. Thus, this article asserts that these two new theoretical contributions make feasible a fundamental advance in the study of collective action.
Rationality in the Cryptographic Model
Hubacek, Pavel
This thesis presents results in the field of rational cryptography. In the first part we study the use of cryptographic protocols to avoid mediation and binding commitment when implementing game theoretic equilibrium concepts. First, we concentrate on the limits of cryptographic cheap talk....... The second part presents a study of the problem of verifiable delegation of computation in the rational setting. We define rational arguments, an extension of the recent concept of rational proofs into the computational setting, and give a single round delegation scheme for the class NC1, of search problems...... computable by log-space uniform circuits of logarithmic depth, with a sub-linear time verifier. While our approach provides a weaker (yet arguably meaningful) guarantee of soundness, it compares favorably with each of the known delegation schemes in at least one aspect. Our protocols are simple, rely...
Monodromy Substitutions and Rational Blowdowns
Endo, Hisaaki; van Horn-Morris, Jeremy
2010-01-01
We introduce several new families of relations in the mapping class groups of planar surfaces, each equating two products of right-handed Dehn twists. The interest of these relations lies in their geometric interpretation in terms of rational blowdowns of 4-manifolds, specifically via monodromy substitution in Lefschetz fibrations. The simplest example is the lantern relation, already shown by the first author and Gurtas to correspond to rational blowdown along a -4 sphere; here we give relations that extend that result to realize the "generalized" rational blowdowns of Fintushel-Stern and Park by monodromy subsitution, as well as several of the families of rational blowdowns discovered by Stipsicz-Szab\\'o-Wahl.
Rational reconstructions of modern physics
Mittelstaedt, Peter
2013-01-01
Newton’s classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of Modern Physics, such as the theory of Special Relativity and Quantum Mechanics. This book shows that, on the basis of Newton’s classical physics and by rational reconstruction, the theory of Special Relativity as well as Quantum Mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results. In the second edition the rational reconstructions are completed with respect to General Relativity and Cosmology. In addition, the statistics of quantum objects is elaborated in more detail with respect to the rational reconstruction of quantum mechanics. The new material completes the approach of t...
The rationing agenda in the NHS. Rationing Agenda Group.
New, B
1996-06-22
The Rationing Agenda Group has been founded to deepen the British debate on rationing health care. It believes that rationing in health care is inevitable and that the public must be involved in the debate about issues relating to rationing. The group comprises people from all parts of health care, none of whom represent either their group or their institutions. RAG has begun by producing this document, which attempts to set an agenda of all the issues that need to be considered when debating the rationing of health care. We hope for responses to the document. The next stage will be to incorporate the responses into the agenda. Then RAG will divide the agenda into manageable chunks and commission expert, detailed commentaries. From this material a final paper will be published and used to prompt public debate. This stage should be reached early in 1997. While these papers are being prepared RAG is developing ways to involve the public in the debate and evaluate the whole process. We present as neutrally as possible all the issues related to rationing and priority setting in the NHS. We focus on the NHS for two reasons. Firstly, for those of us resident in the United Kingdom the NHS is the health care system with which we are most familiar and most concerned. Secondly, focusing on one system alone allows more coherent analysis than would be possible if issues in other systems were included as well. Our concern is with the delivery of health care, not its finance, though we discuss the possible effects of changing the financing system of the NHS. Finally, though our position is neutral, we hold two substantive views--namely, that rationing is unavoidable and that there should be more explicit debate about the principles and issues concerned. We consider the issues under four headings: preliminaries, ethics, democracy, and empirical questions. Preliminaries deal with the semantics of rationing, whether rationing is necessary, and with the range of services to which
Rational economic strategy and entropic analysis
Allred, J.C.; Howard, H.H.
1978-01-01
The neglect of entropic changes of energy and matter in the economic process leads to incorrect formulation of economic theory, as was first pointed out by the economist, Nicholas Georgescu-Roegen. Entropic analysis, that is, the reckoning of entropic changes in real-world processes, appears to be a useful guide toward a realistic understanding of the economic process. The example chosen here is the choice between natural gas and coal as fossil fuel. An outline of the necessary analysis is discussed, together with the requirements of rational economic strategy.
Is Polish Crime Economically Rational?
2010-01-01
This study investigates whether crime in Poland is governed by economic rationality. An economic model of rational behavior claims that the propensity to commit criminal activi-ties is negatively related to deterrence. The potential presence of higher risk profiles for certain population segments is investigated. Panel data aggregated to sub-regional levels and observed annually for the years 2003 to 2005 are applied. Controls for endogeneity among criminal activity level and deterrence, intr...
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
Interpolation of rational matrix functions
Ball, Joseph A; Rodman, Leiba
1990-01-01
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...
Krumpe, M; Brunner, H; Hanami, H; Ishigaki, T; Takagi, T; Markowitz, A G; Goto, T; Malkan, M A; Matsuhara, H; Pearson, C; Ueda, Y; Wada, T
2014-01-01
We present data products from the 300 ks Chandra survey in the AKARI North Ecliptic Pole (NEP) deep field. This field has a unique set of 9-band infrared photometry covering 2-24 micron from the AKARI Infrared Camera, including mid-infrared (MIR) bands not covered by Spitzer. The survey is one of the deepest ever achieved at ~15 micron, and is by far the widest among those with similar depths in the MIR. This makes this field unique for the MIR-selection of AGN at z~1. We design a source detection procedure, which performs joint Maximum Likelihood PSF fits on all of our 15 mosaicked Chandra pointings covering an area of 0.34 square degree. The procedure has been highly optimized and tested by simulations. We provide a point source catalog with photometry and Bayesian-based 90 per cent confidence upper limits in the 0.5-7, 0.5-2, 2-7, 2-4, and 4-7 keV bands. The catalog contains 457 X-ray sources and the spurious fraction is estimated to be ~1.7 per cent. Sensitivity and 90 per cent confidence upper flux limit...
Weesie, H.M.; Snijders, C.C.P.; Buskens, V.W.
2009-01-01
Our research starts from the assumption that actors use a single decision theory to guide them on how to behave in all possible one-shot two-person encounters. To address which decision theories perform well, we let 17 theories compete in a large number of randomly selected symmetric 2 × 2 games. It
Are motorways rational from slime mould's point of view?
Adamatzky, A.; Akl, S.; Alonso-Sanz, R.; van Dessel, W.; Ibrahim, Z.; Ilachinski, A.; Jones, J.; Kayem, A.V.D.M.; Martínez, G.J.; de Oliveira, P.; Prokopenko, M.; Schubert, T.; Sloot, P.; Strano, E.; Yang, X.-S.
2013-01-01
We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK
C语言中浮点数精度问题分析%Analysis on Precision of Floating-point Number for C Language
周冠方
2015-01-01
This article describes how data errors are caused in C language due to different data storage method with case study, an⁃alyses the reason for such errors and explains different storage methods of floating point data in C language. Finally, some sugges⁃tions are proposed in this article.%通过实例直观地描述了C语言中由于计算机存储数据方式的不同而造成的数据误差，并对误差产生的原因进行了分析，解读出C语言中浮点型数据的不同存储方式，最后给出几点建议。
Fukushima, Toshio
2012-11-01
We confirm that the first-, second-, and third-order derivatives of fully-normalized Legendre polynomial (LP) and associated Legendre function (ALF) of arbitrary degree and order can be correctly evaluated by means of non-singular fixed-degree formulas (Bosch in Phys Chem Earth 25:655-659, 2000) in the ordinary IEEE754 arithmetic when the values of fully-normalized LP and ALF are obtained without underflow problems, for e.g., using the extended range arithmetic we recently developed (Fukushima in J Geod 86:271-285, 2012). Also, we notice the same correctness for the popular but singular fixed-order formulas unless (1) the order of differentiation is greater than the order of harmonics and (2) the point of evaluation is close to the poles. The new formulation using the fixed-order formulas runs at a negligible extra computational time, i.e., 3-5 % increase in computational time per single ALF when compared with the standard algorithm without the exponent extension. This enables a practical computation of low-order derivatives of spherical harmonics of arbitrary degree and order.
PVC树脂“鱼眼”数的检测方法研究%STUDY ON TEST METHODS OF DETERMINING THE GEL POINTS NUMBERS OF PVC RESIN
孔秀丽; 李长春; 王晶; 张学明
2012-01-01
研究并总结PVC树脂＂鱼眼＂的检测中遇到的一些问题,结果证明进行PVC树脂＂鱼眼＂检测时,配混料需要放置一段时间再进行塑炼,塑炼温度和切翻次数都会影响＂鱼眼＂数的检测结果,同时要注意＂鱼眼＂的辨别。%This paper studied and summed up many problems in determination of ＂fish eyes＂ for PVC resins. The results proved that when ＂fish eyes＂ being detected, the premixed materials should be kept some time before double -roll blending, both the blending temperature and cut -turning numbers could influence the amounts of ＂fish eye＂, and must pay attention to discern ＂fish eyes＂.
Fyodorov, Yan V; Nadal, Celine
2012-10-19
We exploit a relation between the mean number N(m) of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behavior of N(m) in the simplest glasslike transition occuring in a toy model of a single particle in an N-dimensional random environment, with N>1. Varying the control parameter μ through the critical value μ(c) we analyze in detail how N(m)(μ) drops from being exponentially large in the glassy phase to N(m)(μ)~1 on the other side of the transition. We also extract a subleading behavior of N(m)(μ) in both glassy and simple phases. The width δμ/μ(c) of the critical region is found to scale as N(-1/3) and inside that region N(m)(μ) converges to a limiting shape expressed in terms of the Tracy-Widom distribution.
Obesity, social inequality and economic rationality
Dam, Thea; Jensen, Jørgen Dejgård; Kærgård, Niels
2008-01-01
' utility maximisation behaviour, which all may contribute to explain the ongoing rise in obesity prevalence in many western countries. In addition to standard neoclassical explanations of obesity, we discuss moral hazard aspects, the role of network externalities, self-control problems and habitual......This paper reviews the economic literature related to obesity and consumer decisions, pursuing the overall question, whether the current obesity epidemic and its social bias can be viewed as a result of rational consumption behaviour. We address a number of potential explanations based on consumers...
Torus knots and the rational DAHA
Gorsky, Eugene; Rasmussen, Jacob; Shende, Vivek
2012-01-01
We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m, n) torus knot from the unique finite dimensional simple representation of the rational DAHA of type A, rank n - 1, and central character m/n. The conjectural differentials of Gukov, Dunfield and the third author receive an explicit algebraic expression in this picture, yielding a prescription for the doubly graded Khovanov-Rozansky homologies. We match our conjecture to previous conjectures of the first author relating knot homology to q, t-Catalan numbers, and of the last three authors relating knot homology to Hilbert schemes on singular curves.
Cryptography on elliptic curves over p-adic number fields
XU MaoZhi; ZHAO ChunLai; FENG Min; REN ZhaoRong; YE JiQing
2008-01-01
In this paper we introduce a cryptosystem based on the quotient groups of the group of rational points of an elliptic curve defined over p-adic number field. Some addi-tional parameters are taken in this system, which have an advantage in performing point multiplication while keeping the security of ECC over finite fields. We give a method to select generators of the cryptographic groups, and give a way to represent the elements of the quotient groups with finitely bounded storage by establishing a bijection between these elements and their approximate coordinates. The addition formula under this representation is also presented.
ANTHROPOLOGICAL DESCARTES’ RATIONALISM AND IT'S HUSSERL’S RECEPTION
Anatolii M. Malivskyi
2016-06-01
Full Text Available Purpose. The article is aimed to figure out the features of Husserl's reception of anthropological Descartes rationalism. Its implementation requires a consistent solution of the following tasks: 1 schematically express a modern vision of the basic intentions of philosophizing as an anthropological rationalism; 2 highlight the main points of the Husserl's reception of Descartes’ rationalism as the deanthropologizing and analyze radicalization of its basic design as the reanthropologizing. Conclusions. When clarifying the question of the method of reception and completion of the philosophical Descartes’ project in the doctrine of Edmund Husserl, the author finds that the originality of his reception of anthropological Descartes’ rationalism appears as the paradoxical union of denying the existence of anthropology in the base project and the rediscovery of its key role in the radicalization of Descartes. Thinking of its way, he comes to the rediscovery some of the key ideas of the French philosopher, rooted in his anthropological rationalism. Among them is the basic intention of the ambivalence, the rejection of Descartes’ ideas of panrationalism, recognition irreducibility of philosophical method to the mathematical, constitutive of human presence in the new rationalism. Prospects for further research in understanding the author sees a meaningful relationship and continuity of the two great thinkers - namely, the personal nature of philosophizing and the ethical focus of their searching. Originality. Appeal to the reception of Husserl's Cartesian project confirms the thesis of an essential importance for the basic anthropological project of Descartes. The presented version of Husserl reception base project Descartes is a reproduction of the surface age stereotypes, which link the quest of the philosopher with the natural sciences and neglected anthropological measurements. The proposed version of the radicalization of Descartes’ project
Axioms for Rational Reinforcement Learning
Sunehag, Peter
2011-01-01
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our theory is for complete decision makers, which means that they have a complete set of preferences. Our main result shows that a complete rational decision maker implicitly has a probabilistic model of the environment. We have a countable version of this result that brings light on the issue of countable vs finite additivity by showing how it depends on the geometry of the space which we have preferences over. This is achieved through fruitfully connecting rationality with the Hahn-Banach Theorem. The theory presented here can be viewed as a formalization and extension of the betting odds approach to probability of Ramsey and De Finetti.
Epistemic Immodesty and Embodied Rationality
Giovanni Rolla
Full Text Available ABSTRACT Based on Pritchard's distinction (2012, 2016 between favoring and discriminating epistemic grounds, and on how those grounds bear on the elimination of skeptical possibilities, I present the dream argument as a moderate skeptical possibility that can be reasonably motivated. In order to block the dream argument skeptical conclusion, I present a version of phenomenological disjunctivism based on Noë's actionist account of perceptual consciousness (2012. This suggests that perceptual knowledge is rationally grounded because it is a form of embodied achievement - what I call embodied rationality -, which offers a way of dissolving the pseudo-problem of epistemic immodesty, namely, the seemingly counterintuitive thesis that one can acquire rationally grounded knowledge that one is not in a radical skeptical scenario.
Rational choice in field archaelology
Cătălin Pavel
2011-11-01
Full Text Available In the present article I attempt to apply advances in the study of instrumental and epistemic rationality to field archaeology in order to gain insights into the ways archaeologists reason. The cognitive processes, particularly processes of decision making, that enable archaeologists to conduct the excavation in the trench have not been adequately studied so far. I take my cues from two different bodies of theory. I first inquire into the potential that rational choice theory (RCT may have in modeling archaeological behaviour, and I define subjective expected utility, which archaeologists attempt to maximize, in terms of knowledge acquisition and social gain. Following Elster’s criticism of RCT, I conclude that RCT’s standards for rational action do not correspond with those ostensibly used in field archaeology, but that instrumental rationality has a prominent role in the “archaeological experiment”. I further explore if models proposed as reaction to RCT may account for archaeological decision making. I focus on fast and frugal heuristics, and search for archaeological illustrations for some of the cognitive biases that are better documented in psychological literature. I document confirmation and congruence biases, the endowment effect, observer-expectancy bias, illusory correlation, clustering illusion, sunk cost bias, and anchoring, among others and I propose that some of these biases are used as cognitive tools by archaeologists at work and retain epistemic value. However, I find formal logic to be secondary in the development of archaeological reasoning, with default logic and defeasible logic being used instead. I emphasize scientific knowledge as an actively negotiated social product of human inquiry, and conclude that to describe rationality in field archaeology a bounded rationality model is the most promising avenue of investigation.
Rationalizing the Promotion of Non-Rational Behaviors in Organizations.
Smith, Peter A. C.; Sharma, Meenakshi
2002-01-01
Organizations must balance rational/technical efficiency and emotions. Action learning has been proven to be effective for developing emotional openness in the workplace. Facilitators of action learning should draw upon the disciplines of counseling, Gestalt, psychodynamics, and Eastern philosophies. (Contains 23 references.) (SK)
Mental health as rational autonomy.
Edwards, R B
1981-08-01
Rather than eliminate the terms "mental health and illness" because of the grave moral consequences of psychiatric labeling, conservative definitions are proposed and defended. Mental health is rational autonomy, and mental illness is the sustained loss of such. Key terms are explained, advantages are explored, and alternative concepts are criticized. The value and descriptive components of all such definitions are consciously acknowledged. Where rational autonomy is intact, mental hospitals and psychotherapists should not think of themselves as treating an illness. Instead, they are functioning as applied axiologists, moral educators, spiritual mentors, etc. They deal with what Szasz has called "personal, social, and ethical problems in living." But mental illness is real.
Rational Reconstructions of Modern Physics
Mittelstaedt, Peter
2011-01-01
Newton’s classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of modern physics, such as the theory of relativity and quantum mechanics. This book shows that, on the basis of Newton’s classical physics and by rational reconstruction, the theory of relativity as well as quantum mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results.
胡广垠; 王子欧; 吴升光; 王申卓
2016-01-01
为了对微处理器中浮点运算单元FPU（floating-point unit）进行高效的功能验证，对浮点运算的边界情况进行了研究，引入了对中间结果（intermediate result）的约束解决算法（constriant solved arithmetic）。与传统的对浮点运算单元的功能验证相比，基于该约束算法的浮点数生成器，拓宽了浮点边界情况的可选范围，有效提高了验证效率。实验结果表明，集成该浮点数生成器的UVM验证平台，能够在12小时的测试时间内，对一个浮点运算子模块（floating-point subunit）达到超过99％的覆盖率。%In order to verify the function of the floating-point unit in the microprocessor high-efficiently,numerous corner cases of floating-point arithmetic has been studied.Several arithmetics are introduced to solve the constriants of the intermediate results.Compared with the traditional function verification of floating-point unit,the floating-point number generator based on the constraint solved algorithms has widened the scope of the optional floating-point corner cases,which effectively improves the verification efficiency.Experimental results show that the UVM verification platform which integrated the generator can test one floating-point subunit efficiently,which achieves high coverage beyond 98%,within 12 hours of testing time.
MOK Ngaiming
2008-01-01
In 1993,Tsai proved that a proper holomorphic mapping f : Ω→Ω' from an irreducible bounded symmetric domain Ω of rank ≥ 2 into a bounded symmetric domain Ω' is necessarily totally geodesic provided that r' : = rank(Ω') ≤ rank(Ω) := r,proving a conjecture of the author's motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents (VMRTs).In another completely different direction Hwang-Mok established with very few exceptions the Cartan-Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num-ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio-nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com-plex Grassmahn manifolds of rank ≤ 2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin's which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures.
Algebraic points on meromorphic curves
Herblot, Mathilde
2012-01-01
The classic Schneider-Lang theorem in transcendence theory asserts that there are only finitely many points at which algebraically independent complex meromorphic functions of finite order of growth can simultaneously take values in a number field, when satisfying a polynomial differential equation with coefficients in this given number field. In this article, we are interested in generalizing this theorem in two directions. First, instead of considering meromorphic functions on C we consider holomorphic maps on an affine curve over the field C or C_p. This extends a statement of D. Bertrand, which applies to meromorphic functions on P^1(C) or P^1(C_p) minus a finite subset of points. Secondly, we deal with algebraic values taken by the functions, instead of rational values as in the classic setting, inspired by a work of D. Bertrand. We prove a geometric statement extending those two results, using the slopes method, written in the language of Arakelov geometry. In the complex case, we recover a special case...
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
Optimal public rationing and price response.
Grassi, Simona; Ma, Ching-To Albert
2011-12-01
We study optimal public health care rationing and private sector price responses. Consumers differ in their wealth and illness severity (defined as treatment cost). Due to a limited budget, some consumers must be rationed. Rationed consumers may purchase from a monopolistic private market. We consider two information regimes. In the first, the public supplier rations consumers according to their wealth information (means testing). In equilibrium, the public supplier must ration both rich and poor consumers. Rationing some poor consumers implements price reduction in the private market. In the second information regime, the public supplier rations consumers according to consumers' wealth and cost information. In equilibrium, consumers are allocated the good if and only if their costs are below a threshold (cost effectiveness). Rationing based on cost results in higher equilibrium consumer surplus than rationing based on wealth.
Teaching Rational Decision-Making.
Woolever, Roberts
1978-01-01
Presented is an outline of a college course, "Education in American Society," that focused on teaching students rational decision-making skills while examining current issues in American Education. The outline is followed by student comments, reactions, and evaluations of the course. (JMD)
Rational Exponentials and Continued Fractions
Denny, J. K.
2012-01-01
Using continued fraction expansions, we can approximate constants, such as pi and e, using an appropriate integer n raised to the power x[superscript 1/x], x a suitable rational. We review continued fractions and give an algorithm for producing these approximations.
Personal Autonomy and Rational Suicide.
Webber, May A.; Shulman, Ernest
That certain suicides (which can be designated as rational) ought not to be interfered with is closely tied to the notion of the "right to autonomy." Specifically it is because the individual in question has this right that interference is prohibited. A proper understanding of the right to autonomy, while essential to understanding why suicide is…
Rational Normalization of Concentration Measures.
Bonckaert, P.; Egghe, L.
1991-01-01
Discusses normalization features of good concentration measures and extends the range of values of concentration measures that are population-size-independent. Rational normalization is described, and mathematical formulas for the coefficient of variation, Pratt's measure, the Gini index, Theil's measure, and Atkinson's indices are explained. (14…
王宇航; 缪亚敏; 杨昕
2012-01-01
为了研究采样点数目对反距离加权插值结果的影响,以面积为2.076x105km2的白俄罗斯为研究区域,采用数目逐渐变化的采样点作为实验数据,通过交叉验证方法,得到了采样点数目与插值精度之间的关系.结果表明:随着采样点数目减少,插值误差呈现先缓慢上升后迅速上升再缓慢上升的趋势.就本组数据而言,当采样点逐渐减少到约为总采样点数目的70％左右,插值的质量会发生突变.计算采样点的密度,得出每100km2采0.9～1.3个点(即每76～109km2采集1个点)的情况下,插值精度变化不大.鉴于研究所得,在实际的生产生活中,可供大区域插值时,采样方案设计参考.%In order to research the impact of the sampling point number on the precision of the inverse distance weighted interpolation, we take the territory of Belarus as research area whose acreage is two hundred thousand seven thousand and six hundred square kilometers. By gradually changing the number of the sampling points which is regarded as experimental data, we adopt cross-validation method to acquire the quantitative relationship between the sampling point number and the interpolation precision. The results illustrate that with the decreasing number of sampling points, interpolation error shows the trend that it will rise slowly in the beginning, and then the rise accelerate, eventually it rises slowly again. As concerned of this group of data, when the number of the experimental points gradually reduces to about seventy percent of total of the sample points, the interpolation quality will mutate. Through calculating density of sample points, we can get a conclusion that when of sampling point number is from 0.9 to 1.3 per 100 km2 (that is to say one sampling point is collected per 76-109 km2), the interpolation precision changes slightly. According to this study, during the daily production, the result will be a reference for the interpolation of large area.
The dynamics of Bertrand model with bounded rationality
Zhang Jixiang [School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189 (China)], E-mail: zhang_jixiang@126.com; Da Qingli [School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189 (China); Wang Yanhua [School of Environmental Science and Engineering, Shanghai Jiao Tong University Min Hang, Shanghai 200240 (China)
2009-03-15
The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.
On integrable rational potentials of the Dirac equation
Stachowiak, Tomasz, E-mail: stachowiak@cft.edu.pl [Center for Theoretical Physics PAS, Al. Lotnikow 32/46, 02-668 Warszawa (Poland); Przybylska, Maria, E-mail: M.Przybylska@proton.if.uz.zgora.pl [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland)
2013-05-03
The one-dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the results have to be stated with recursive relations, because in general the equation is of Heun type. The inverse problem of finding integrable rational potentials based on the properties of the singular points is also presented; in particular, a general class of integrable potentials leading to the Whittaker equation is found.
[Rational drug use: an economic approach to decision making].
Mota, Daniel Marques; da Silva, Marcelo Gurgel Carlos; Sudo, Elisa Cazue; Ortún, Vicente
2008-04-01
The present article approaches rational drug use (RDU) from the economical point of view. The implementation of RDU implies in costs and involves acquisition of knowledge and behavioral changes of several agents. The difficulties in implementing RDU may be due to shortage problems, information asymmetry, lack of information, uncertain clinical decisions, externalities, time-price, incentives for drug prescribers and dispensers, drug prescriber preferences and marginal utility. Health authorities, among other agencies, must therefore regularize, rationalize and control drug use to minimize inefficiency in pharmaceutical care and to prevent exposing the population to unnecessary health risks.
Đorđević Đorđe
2015-01-01
Full Text Available This paper examines the impact of various object-to-camera distances and the number of station-points i.e. various shooting directions with regard to the obtained Density-quality of photogrammetrically created Point-clouds - as digital representations of the existent linear architectural/urban objects/elements. According to an artificial (purified experimental scene used, the conclusion is that with the chosen focal lengths/object-to-camera distances, with shooting directions perpendicular to the axis of that object, with station-points uniformly radially distributed around it (at a circle of 360deg, and with the obtained values of photogrammetric-software process-quality outputs which belong to the recommended ranges, the achieved density-level of the created Point-clouds may be treated as independent on the camera's radial-movement angle but dependent on the percentage of „Object's Photo-Coverage”: the lower the Coverage, the lower the density. Also, regardless of the Coverage level, the majority of the generated points are generally more "densimetrically" precise than they are "densimetrically" accurate.
Are investors rational, irrational or normal?
Md Al Mamun
2015-08-01
Full Text Available The nature of investor’s rationality vs. irrationality debate drawn attention of thousands of academic papers, hundreds of conferences, roundtables discussion leading to two ends: the classical theorist i.e. the proponents of efficient market hypothesis (EMH and the behaviorist. From Fisher’s (1906 Nature of Capital & Income to Ross (1977; investor’s rationality has been considered as the principal assumption in the development of theoretical finance. Unfortunately though, various studies have shown repeated form of investor’s irrationality and incompetence in their decision process. Even the very proponents of EMH, Fama (1965 has later on in 1993 advocated the lack of market efficiency! Indeed the story of black Monday in the USA to the global financial tsunami (2007-2012 has put the proponents of EMH into the cluelessness. While, the behaviorists argument that the financial markets can be best understood by studying the psychology is also subject to criticism that there will be no existence of standard models to study agent’s behavior in the market! Therefore, this study aims at finding out the true scenarios of investor’s behavior by working on 200 individual investors in Dhaka Stock Exchange (DSE. Investors’ response to different questions relating to fundamental assumption of “rationality’ or ‘presence of irrationality." The result shows a complete absence of the assumption of rationality or irrationality in number of critical issues. Therefore, the idea of EMH or mere psychologically driven behavioral finance should become less acknowledgeable in understanding the agents of financial market i.e. the investors. Rather a combination of these two may give more insight in understanding the investor’s behavior in the financial market.
ISOGENOUS OF THE ELLIPTIC CURVES OVER THE RATIONALS
Abderrahmane Nitaj
2002-01-01
An elliptic curve is a pair (E, O), where E is a smooth projective curve of genus 1 and O is a point of E, called the point at infinity. Every elliptic curve can be given by a Weierstrass equationE: y2 + a1xy + a3y = x3 + a2x2 + a4x + a6.Let Q be the set of rationals. E is said to be difined over Q if the coefficients ai, i =1, 2, 3, 4, 6 are rationals and O is defined over Q.Let E/Q be an elliptic curve and let E(Q)tors be the torsion group of points of E defined over Q. The theorem of Mazur asserts that E(Q)tors is one of the following 15 groupsWe say that an elliptic curve E′/Q is isogenous to the elliptic curve E if there is an isogeny,i.e. a morphism φ: E → E′ such that φ(O) = O, where O is the point at infinity.We give an explicit model of all elliptic curves for which E(Q)tors is in the form Z/mZ where m = 9, 10, 12 or Z/2Z × Z/2mZ where m = 4, according to Mazur's theorem.Morever, for every family of such elliptic curves, we give an explicit model of all their isogenous curves with cyclic kernels consisting of rational points.
The Competency of Rational Silent Reading, Its Synthesized Development
Vytautas Šernas
2011-04-01
Full Text Available The European Board documents [6] approved by the Ministry of Education [7, 8] orient the European countries, teachers to ensure a very good, masterful acquisition of three languages (Vantage B2. This attitude is related to an individual’s acquired level of the rational silent reading. The author has been interested in the problem of rational silent reading for 35 years. In the empirical research and experiments there took part more than 500 pupils, students, teachers, employees of different spheres, secondary schools graduates. From the point of view of rational silent reading Lithuania is significantly lagging behind other countries. There are many reasons for that. In order to highlight them there has been briefly studied the content of the rational silent reading according to B2 level; touched on the most significant dimensions of this competency, reviewed the consistent patterns and content of the teaching and learning process of the rational silent reading as well as the norms of such reading in Lithuanian, English, Russian, French. Some research results are presented. At the end there has been given the whole mosaic of recommendations, based on the research, different glottoeducological, psychological, psycholinguistic, physiological, linguistic, etc literature. The aim of the article is to invite teachers, scientists to participate actively in this problem solution under the new Lithuanian conditions.
Professor Stewart's incredible numbers
Stewart, Ian
2015-01-01
Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,
WAVELET RATIONAL FILTERS AND REGULARITY ANALYSIS
Zheng Kuang; Ming-gen Cui
2000-01-01
In this paper, we choose the trigonometric rational functions as wavelet filters and use them to derive various wavelets. Especially for a certain family of wavelets generated by the rational filters, the better smoothness results than Daubechies' are obtained.
Rationality, mental causation and social sciences
Mladenović Ivan
2009-01-01
Full Text Available The aim of this paper is to investigate the role of mental causation in the context of rational choice theory. The author defends psychological aspect of rational explanation against the challenge of contemporary reductive materialism.
A Rational Approach to Cryptographic Protocols
Caballero-Gil, P; Bruno-Castañeda, C; 10.1016/j.mcm.2006.12.013
2010-01-01
This work initiates an analysis of several cryptographic protocols from a rational point of view using a game-theoretical approach, which allows us to represent not only the protocols but also possible misbehaviours of parties. Concretely, several concepts of two-person games and of two-party cryptographic protocols are here combined in order to model the latters as the formers. One of the main advantages of analysing a cryptographic protocol in the game-theory setting is the possibility of describing improved and stronger cryptographic solutions because possible adversarial behaviours may be taken into account directly. With those tools, protocols can be studied in a malicious model in order to find equilibrium conditions that make possible to protect honest parties against all possible strategies of adversaries.
Tangency quantum cohomology and characteristic numbers
KOCK JOACHIM
2001-01-01
Full Text Available This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincaré metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.
On a Graphical Technique for Evaluating Some Rational Expectations Models
Johansen, Søren; Swensen, Anders R.
2011-01-01
. In addition to getting a visual impression of the fit of the model, the purpose is to see if the two spreads are nevertheless similar as measured by correlation, variance ratio, and noise ratio. We extend these techniques to a number of rational expectation models and give a general definition of spread...
Sierpinski and Carmichael Numbers
2013-01-16
appear. 31 [21] E. M. Matveev, ‘An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II,’ Izv. Ross. Akad...Math. Comp. 37 (1981), 587–593. [23] C. Pontreau, ‘A Mordell- Lang plus Bogomolov type result for curves in G2m,’ Monatsh. Math. 157 (2009), 267–281. [24
Psychology and the Rationality of Emotion*
Clore, Gerald L.
2011-01-01
Questions addressed by recent psychological research on emotion include questions about how thought shapes emotion and how emotion, in turn, shapes thought. Research on emotion and cognition paints a somewhat different picture than that seen in traditional discussions of passion and reason. This article reviews several aspects of this research, concentrating specifically on three views of rationality: Rationality as Process, Rationality as Product, and Rationality as Outcome.
Kant on empiricism and rationalism
Vanzo, Alberto
2013-01-01
This paper aims to correct some widely held misconceptions concerning Kant's role in the formation of a widespread narrative of early modern philosophy. According to this narrative, which dominated the English-speaking world throughout the twentieth century, the early modern period was characterized by the development of two rival schools: René Descartes's, Baruch Spinoza's, and G. W. Leibniz's rationalism; and John Locke's, George Berkeley's, and David Hume's empiricism. Empiricists and rati...
Davidson on Turing: Rationality Misunderstood?
John-Michael Kuczynski
2005-12-01
Full Text Available Alan Turing advocated a kind of functionalism: A machine M is a thinker provided that it responds in certain ways to certain inputs. Davidson argues that Turing’s functionalism is inconsistent with a cer-tain kind of epistemic externalism, and is therefore false. In Davidson’s view, concepts consist of causal liasons of a certain kind between subject and object. Turing’s machine doesn’t have the right kinds of causal li-asons to its environment. Therefore it doesn’t have concepts. Therefore it doesn’t think. I argue that this reasoning is entirely fallacious. It is true that, in some cases, a causal liason between subject and object is part of one’s concept of that object. Consequently, to grasp certain propositions, one must have certain kids of causal ties to one’s environment. But this means that we must rethink some old views on what rationality is. It does not mean, pace Davidson, that a precondition for being rational is being causally embedded in one’s environment in a certain way. If Tur-ing’s machine isn’t capable of thinking (I leave it open whether it is or is not, that has nothing to do with its lacking certain kinds of causal con-nections to the environment. The larger significance of our discussion is this: rationality consists either in one’s ability to see the bearing of purely existential propositions on one another or rationality is simply not to be understood as the ability see the bearing that propositions have on one another.
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Bounded rationality and heterogeneous expectations in macroeconomics
D. Massaro
2012-01-01
This thesis studies the effect of individual bounded rationality on aggregate macroeconomic dynamics. Boundedly rational agents are specified as using simple heuristics in their decision making. An important aspect of the type of bounded rationality described in this thesis is that the population of
Rational Solutions in a Coupled Burgers System
HUANG Ling
2006-01-01
Three types of the rational solutions for a new coupled Burgers system are studied in detail in terms of the reduction and decoupled procedures. The first two types of rational solutions are singular and valid for one type of model parameter c＞0, and another type of rational solutions is nonsingular at any type and valid for another type of model parameter c＜0.
Rational Thinking in School-Based Practice
Clark, Mary Kristen; Flynn, Perry
2011-01-01
Purpose: We reflect on Alan Kamhi's (2011) prologue on balancing certainty and uncertainty as it pertains to school-based practice. Method: In schools, rational thinking depends on effective team processes, much like professional learning communities. We consider the conditions that are required for rational thinking and how rational team dialogue…
Distribution theory of algebraic numbers
Yang, Chung-Chun
2008-01-01
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.
Rational trigonometric approximations using Fourier series partial sums
Geer, James F.
1993-01-01
A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.
Application of SharePoint Portal Technologies in Public Enterprises
Dragan Đokić
2015-03-01
Full Text Available Nowadays, systematic reforms are realized acrossmany countries. One of the characteristics of these reforms is necessity for rationalization of expenses in governmental and public enterprises. Rationalization of expenses can be achieved by more extensive application of information and communication technologies based on internet technologies and cloud computing. These systems include huge number of services, applications, resources, users and roles. At the same time, concepts of scalability, availability, ubiquity and pervasiveness need to be applied. This paper deals with application of portal technologies for enhanced content management, document management, and collaboration within public enterprises. The goal is to achieve efficient exchange of information on all hierarchical levels, as well as mechanisms of reporting and performance measurements, such as business intelligence and key performance indicators. The model is based on SharePoint portal technologies. A case study of application within the public enterprise Post of Serbia is described.
DETERMINANTS OF RATIONAL-IRRATIONAL CONSUMPTION AND RESEARCH IN ISPARTA
Zafer YILDIZ
2015-08-01
Full Text Available Consumption means that depleting the product or service by using it. Each one has to consume to sustain their life. The increase in the number and diversity of goods and services that meet needs by emerging technology over time has brought with it the obligation to electing and decision-making while consuming them. People remain under the influence of many internal and external factors while consuming and they make consumption decisions under the same influences. In this case, the consumption moves away from rationality time to time. Internal and external factors affecting the consumer decisions and how they affect the consumption must be known to understand consumption is rational or not. This study was carried out for research the factors that caused the consumption is rational or irrational. The data were collected through face to face interviews from the sample group of 205 people in Isparta centrum. The obtained data were entered into SPSS software in an appropriate format and analyzes such as reliability, factor and correlation were performed. As a result of the analysis, the factors affecting the human's consumption rationality are divided into two groups as rational and irrational by the interpretation of findings. Also, information about consumption behaviors of the respondents has been reached by applying the Crosstab analysis to data.
Multi-Parameter Sampling for Rational Languages
Bodini, Olivier
2010-01-01
This paper addresses how to efficiently sample words from a rational language (over an alphabet of size $k$), while constraining every letter to a targeted frequencies of occurrence. Our approach consists in an extended -- multivariate -- version of the classical Boltzmann samplers \\cite{Duchon2004}. We prove that, under relatively weak hypotheses, our sampler returns a word of size in $[(1-\\epsilon)n, (1+\\epsilon)n]$ and exact frequency in $\\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept a tolerance interval of length in $\\mathcal{O}(\\sqrt{n})$ for the number of occurrences of each letters, our sampler reaches an approximate-size generation of words in expected $\\mathcal{O}(n)$ time. We illustrate these techniques on the generation of perfect Tetris histories (Tesselations of a $w\\times h$ rectangle).
Rational choice theory and suicide.
Lester, D
1988-12-01
The implications of viewing the decision to kill oneself as a rational choice, based on an analysis of the costs and benefits, were explored. Suicide is but one symptom for an individual in distress to choose, and if suicide is prevented, other symptoms may appear in its place. Similarly, a critical question to be asked in suicide prevention is whether restriction of the availability of one method for suicide (such as detoxifying domestic gas or car exhaust) will result in suicidal individuals switching to a different method for suicide or to a different symptom of distress.
Reconciling Psychology with Economics - Obesity, Behavioral Biology, and Rational Overeating
Trenton Smith
2006-01-01
Reconciling Psychology with Economics: Obesity, Behavioral Biology, and Rational Overeating Abstract: The modern phenomenon of obesity is an archetypal example of a behavior whose explanation simultaneously falls within the purview of psychology, economics, and the biological sciences. While psychologists and advocates of public health have long viewed overeating as a weakness or disease in need of treatment, economists have pointed out that "like any other consumer behavior" choices about di...
Reappraisal of Rational Choice Theory
Katalin Martinas
2013-01-01
Full Text Available The value of rational choice theory (RCT for the social sciences has long been contested. Much time has been spent by economists and critics on the pervasive but elusive concept of rationality. The critiques mainly challenge the basis of the utility theorem. Several articles on the misuse of mathematics in economics have already appeared in the literature. As N. Bouleau stated, “On several occasions, however, one feels that the criticism is that the math is being misused and should be developed in some other direction (e.g. a statistical analysis of the financial tendencies that polarize wealth and income, or a study of the positive feedback mechanisms, etc.. This leaves certain dissatisfaction – on a philosophical level.” The aim of this paper is to present a decision theory, yields intention (logos and valuation (existence. Here we present a new mathematical representation of RCT, which leads to a dynamic economic theory. We discuss the philosophical or meta-economical problems, which are needed for the successful applications of mathematics.
Rational approximations to fluid properties
Kincaid, J. M.
1990-05-01
The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function tilde p(T,rho) that contains a set of parameters (gamma sub i); the (gamma sub i) is chosen such that tilde p(T,rho) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and rho is the density). In most cases, a nonlinear least-squares numerical method is used to determine (gamma sub i). There are several drawbacks to this method: one has essentially to guess what tilde p(T,rho) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular, it lets the data choose the function tilde p(T,rho) and its numerical implementation involves only linear algorithms.
Derivation of Invariant Varieties of Periodic Points from Singularity Confinement
Yumibayashi, Tsukasa; Wakimoto, Yuki
2011-01-01
It was shown, in our previous works, that periodic points of $d$ dimensional rational integrable maps form varieties if the number of invariants $p$ is greater than $d/2$. In the case of 3 dimensional Lotka-Volterra map with 2 invariants the varieties are generated iteratively by the map after it is recovered from the singularity confinement. We present many other examples of this phenomenon in this paper when $p=d-1$, and discuss how to generalize our algorithm when $p$ is less than $d-1$.
Rips, Lance J; Thompson, Samantha
2014-03-01
Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Mehtap Sahingoz
2013-02-01
Full Text Available ABSTRACT Objective: At this study to be aimed to assess status of the knowledge of nurses who working in public and private health institutions in Sivas province use of medication fort he treatment during their illnesses and patients and the attitudes of rational drug application. Matherials and methods: the researc planned to attend 750 nurses but it has been completed with participation of 641 nurses (Reaching rate 85,5%. This is a descriptive and cross-sectional study. in the study data were collected with a questionaire, percentages stated and chi square test was used for analysis. Results: %95,3 of nurses were females and mean age of them 29.21±4.85 years. The rate of contacting a doktor in case of illness is higher in 39.1% of nurses in the 21-30 age group and 48.6% of nurses working in primary care institutions. The level of self-treating is higher in 45.5 % of nurses working less than a year in profession .In the case of illness, 53% of nurses stated that they had left the medicine when signs of disease over. %98.8 of nurses expressed that they know effects of drugs used and 99.1% of them stated they know the side effects of drugs used. The entire group of postgraduate education status stated that they have not received the drug recommended by others. The level of suggesting a drug to someone else fort he same disease is higher in 65.8% of the group 31 years and older and group working over 40 hours per week. It were determined that used in consultation with the physician 65.2% of nurses antibiotics, 87.5% of them weiht loss drug and 82.7% of them contraceptive . 99.5% of the nurses have expressed that they inform to patients about use of their medications. Among the issues that expressed informations took place the application form of drugs (51.0 %and information of need to consult one if deemed one unexpected effect (59.6% . Also has been identified that of nurses acquired inform about drugs from drug book (vademecum (87.5 % and they
Rational Choice and the Framing of Decisions.
1986-05-29
Yellen, J. (1985). Can small deviations from rationality make significant differences to economic equilibria? American Economic Review , 75, 708-720...theory of choice and the preference reversal phenomenon. American Economic Review , 69, 623-38. Hagen, 0. (1979). Towards a positive theory of preferences...Publishing Co. Haltiwanger, J. & Waldman, M. (1985). Rational expectations and the limits of rationality: An analysis of heterogeneity. American Economic Review , 75
Rational Addiction Evidence From Carbonated Soft Drinks
Xiaoou, Liu
2009-01-01
This paper applies the Becker-Murphy (1988) theory of rational addiction to the case of carbonated soft drinks, using a time-varying parameter model and scanner data from 46 U.S. cities. Empirical results provide strong evidence that carbonated soft drinks are rationally addictive, thus opening the door to taxation and regulation. Taking rational addition into account, estimated demand elasticities are much lower than previous estimates using scanner data.
The structure of bivariate rational hypergeometric functions
Cattani, Eduardo; Villegas, Fernando Rodriguez
2009-01-01
We describe the structure of all codimension-two lattice configurations $A$ which admit a stable rational $A$-hypergeometric function, that is a rational function $F$ all whose partial derivatives are non zero, and which is a solution of the $A$-hypergeometric system of partial differential equations defined by Gel'fand, Kapranov and Zelevinsky. We show, moreover, that all stable rational $A$-hypergeometric functions may be described by toric residues and apply our results to study the rationality of bivariate series whose coefficients are quotients of factorials of linear forms.
RATIONAL PHARMACOTHERAPY IN TAKOTSUBO CARDIOMYOPATHY
S. Marchev
2012-01-01
Full Text Available Rational pharmacotherapy in Takotsubo cardiomyopathy is based on clinical picture and data of functional and laboratory investigations of concrete patient. In patients with hypotension and moderate-to-severe left ventricle outflow tract obstruction inotropic agents must not to be used because they can worsen the degree of obstruction. In these patients beta blockers can improve hemodynamics by causing resolution of the obstruction. If intraventricular thrombus is detected, anticoagulation for at least 3 months is recommended. The duration of anticoagulant therapy may be modified depending on the extent of cardiac function recovery and thrombus resolution. For patients without thrombus but with severe left ventricular dysfunction, anticoagulation is recommended until the akinesis or dyskinesis has resolved but not more than 3 months.
Dual Rationality and Deliberative Agents
Debenham, John; Sierra, Carles
Human agents deliberate using models based on reason for only a minute proportion of the decisions that they make. In stark contrast, the deliberation of artificial agents is heavily dominated by formal models based on reason such as game theory, decision theory and logic—despite that fact that formal reasoning will not necessarily lead to superior real-world decisions. Further the Nobel Laureate Friedrich Hayek warns us of the ‘fatal conceit’ in controlling deliberative systems using models based on reason as the particular model chosen will then shape the system’s future and either impede, or eventually destroy, the subtle evolutionary processes that are an integral part of human systems and institutions, and are crucial to their evolution and long-term survival. We describe an architecture for artificial agents that is founded on Hayek’s two rationalities and supports the two forms of deliberation used by mankind.
Essays on Rational Portfolio Theory
Nielsen, Simon Ellersgaard
This dissertation is comprised of five research papers written during the period January 2013 -December 2015. Their abstracts are: The Fundamental Theorem of Derivative Trading. When estimated volatilities are not inperfect agreement with reality, delta hedged option portfolios will incur a non...... is proportional to volatility, we can deriveclosed form expressions for the optimal portfolio using the formalism of Hamilton-JacobixiiiBellman. We also perform an empirical investigation, which strongly suggests that there inreality are no tangible welfare gains associated with hedging stochastic volatility...... in a bondstockeconomy. Stochastic Volatility for Utility Maximisers Part II. Using martingale methods we derivebequest optimising portfolio weights for a rational investor who trades in a bond-stockderivativeeconomy characterised by a generic stochastic volatility model. For illustrativepurposes we then proceed...
Silverman, Joseph H
2011-01-01
Let F : P^N --> P^N be a dominant rational map. The dynamical degree of F is the quantity d_F = lim (deg F^n)^(1/n). When F is defined over a number field, we define the arithmetic degree of an algebraic point P to be a_F(P) = limsup h(F^n(P))^(1/n) and the canonical height of P to be h_F(P) = limsup h(F^n(P))/n^k d_F^n for an appropriately chosen integer k = k_F. In this article we prove some elementary relations and make some deep conjectures relating d_F, a_F(P), and h_F(P). We prove our conjectures for semisimple monomial maps.
Hodograph computation and bound estimation for rational B-spline curves
无
2007-01-01
It is necessary to compute the derivative and estimate the bound of rational B-spline curves in design system, which has not been studied to date. To improve the function of computer aided design (CAD) system, and to enhance the efficiency of different algorithms of rational B-spline curves, the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational B-spline curves are derived by applying Dir function, which indicates the direction of Cartesian vector between homogeneous points, discrete B-spline theory and the formula of translating the product into a summation of B-spline functions. As an application of the result above,upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.
Tuckman, Bruce W
2005-06-01
This study compared students' academic procrastination tendency with the (1) frequency and nature of rationalizations used to justify procrastination, (2) self-regulation, and (3) performance in a web-based study strategies course with frequent performance deadlines. 106 college students completed the 16-item Tuckman Procrastination Scale, a measure of tendency to procrastinate, the Frequency of Use Self-survey of Rationalizations for Procrastination, and a 9-item self-regulation scale. Students' subsequent course performance was measured by total points earned. A linear regression with Academic Procrastination as the criterion variable and Rationalization score and Course Points as the predictor variables suggested academic procrastinators support procrastinating by rationalizing, not self-regulating, and thus put themselves at a disadvantage, with respect to evaluation in highly structured courses with frequent enforced deadlines.
Kalberg, Stephen
1980-01-01
Explores rationality in Max Weber's works and identifies four types of rationality which play major roles in his writing--practical, theoretical, substantive, and formal. Implications for society and education are discussed. (DB)
A tale of paradigm clash: Simon, situated cognition and the interpretation of bounded rationality
2015-01-01
The intellectual figure of Herbert A. Simon is well known for having introduced the influential notion of bounded rationality in economics. Less known, at least from the economists’ point of view, is the figure of Simon as eminent cognitive psychologist, co-founder of so-called cognitivism, a mainstream approach in cognitive psychology until the 80s of the last century. In fact, the two faces of Simon’s intellectual figure, as rationality scholar and as cognitive scientist, are not factorizab...
A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm
Godfrey Chagwiza
2016-01-01
Full Text Available In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.
Criteria for rational smoothness of some symmetric orbit closures
Hultman, Axel
2009-01-01
Let $G$ be a connected reductive linear algebraic group over $\\C$ with an involution $\\theta$. Denote by $K$ the subgroup of fixed points. In certain cases, the $K$-orbits in the flag variety $G/B$ are indexed by the twisted identities $\\iot = \\{\\theta(w^{-1})w\\mid w\\in W\\}$ in the Weyl group $W$. Under this assumption, we establish a criterion for rational smoothness of orbit closures which generalises classical results of Carrell and Peterson for Schubert varieties. That is, whether an orbit closure is rationally smooth at a given point can be determined by examining the degrees in a ``Bruhat graph'' whose vertices form a subset of $\\iot$. Moreover, an orbit closure is rationally smooth everywhere if and only if its corresponding interval in the Bruhat order on $\\iot$ is rank symmetric. In the special case $K=\\Sp_{2n}(\\C)$, $G=\\SL_{2n}(\\C)$, we strengthen our criterion by showing that only the degree of a single vertex, the ``bottom one'', needs to be examined. This generalises a result of Deodhar for type ...
The Rationality of Alcoholics Anonymous and the Spirituality of Rational Emotive Behavior Therapy.
Velten, Emmett
1996-01-01
Argues that Alcoholics Anonymous (AA) and Rational Emotive Behavior Therapy (REBT) share important rational objectives and numerous cognitive-behavioral methods. Both emphasize a philosophical shift as a principal ingredient for change. Provides definitions of rationality and spirituality and explains how REBT and smart recovery are spiritual…
The Rationality of Alcoholics Anonymous and the Spirituality of Rational Emotive Behavior Therapy.
Velten, Emmett
1996-01-01
Argues that Alcoholics Anonymous (AA) and Rational Emotive Behavior Therapy (REBT) share important rational objectives and numerous cognitive-behavioral methods. Both emphasize a philosophical shift as a principal ingredient for change. Provides definitions of rationality and spirituality and explains how REBT and smart recovery are spiritual…
Rationality and Belief in Learning Mathematics
Brown, Tony
2016-01-01
This paper argues that rationality and belief are mutually formative dimensions of school mathematics, where each term is more politically embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a particular…
Linear parameter estimation of rational biokinetic functions
Doeswijk, T.G.; Keesman, K.J.
2009-01-01
For rational biokinetic functions such as the Michaelis-Menten equation, in general, a nonlinear least-squares method is a good estimator. However, a major drawback of a nonlinear least-squares estimator is that it can end up in a local minimum. Rearranging and linearizing rational biokinetic
曹俊鹏; 侯伯宇; 岳瑞宏
2001-01-01
We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N) Gaudin model based onthe quasi-classical limit of the SU ( N) chain under the periodic boundary condition. Using the quantum inversescattering method, we also obtain the eigenvalues of the generation function of the rational SU ( N) Gaudin model.
Empirical Rationality in the Stock Market
Raahauge, Peter
2003-01-01
for this empiricalrationality on part of the agent, the resulting empirical model assignslikelihood to the data actually observed, unlike in the unmodified rational expectationscase. A Lucas (1978)-type asset pricing model which incorporatesempirical rationality is constructed and estimated using U.S. stock data...
Is facet analysis based on rationalism?
Hjørland, Birger
2014-01-01
, rationalism, historicism/hermeneutics, or pragmatism/critical theory (of which only the last position fully acknowledges the non-neutrality of knowledge organisation). Ranganathan – and the whole facet-analytic school – has formerly been exemplified as a rather clear example of rationalism. Some have objected...
Are Grade Expectations Rational? A Classroom Experiment
Hossain, Belayet; Tsigaris, Panagiotis
2015-01-01
This study examines students' expectations about their final grade. An attempt is made to determine whether students form expectations rationally. Expectations in economics, rational or otherwise, carry valuable information and have important implications in terms of both teaching effectiveness and the role of grades as an incentive structure for…
The Problem of Rational Moral Enlistment
Tillson, John
2017-01-01
How can one bring children to recognize the requirements of morality without resorting only to non-rational means of persuasion (i.e. what rational ground can be offered to children for their moral enlistment)? Michael Hand has recently defended a foundationalist approach to answering this question and John White has responded by (a) criticizing…
Neurophysiology and Rationality in Political Thinking.
Peterson, Steven A.
Research both in cognitive psychology and psychobiology suggests that political behavior is often less rational than individuals believe it to be. Information processing, memory, and decision making are interlinked processes. Studies in cognitive psychology reveal that even though decision making requires rationality, individuals often adopt…
Rationality and Belief in Learning Mathematics
Brown, Tony
2016-01-01
This paper argues that rationality and belief are mutually formative dimensions of school mathematics, where each term is more politically embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a particular…
Rationality : a social-epistemology perspective
Wenmackers, Sylvia; Vanpoucke, Danny E. P.; Douven, Igor
2014-01-01
Both in philosophy and in psychology, human rationality has traditionally been studied from an “individualistic” perspective. Recently, social epistemologists have drawn attention to the fact that epistemic interactions among agents also give rise to important questions concerning rationality. In pr
The rational emotions of FC København
Storm, Rasmus K.
2009-01-01
Professional team sports clubs in Scandinavia and Europe operate in a complex combination of rational economic logic and emotional irrational behaviour. With a few exceptions most clubs favour winning over profit, thus producing a range of severe financial problems as a direct consequence...... performers in the sports business, I explain why only a few clubs are capable of combining economic gain with sporting success. The Danish soccer club FC K benhavn is chosen to be the case and turning point in this study, as it serves as a counter example illustrating how profit and championships can...... actually be combined in certain logic of 'rational emotionality'. The 'extremity' of the case in this respect serves as a way to expose the general rules of commercial sports....
Generalized NLS Hierarchies from Rational $W$ Algebras
Toppan, F
1994-01-01
Finite rational $\\cw$ algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. In this letter we address the problem of relating these algebras to integrable hierarchies of equations, by showing how to associate to a rational $\\cw$ algebra its corresponding hierarchy. We work out two examples: the $sl(2)/U(1)$ coset, leading to the Non-Linear Schr\\"{o}dinger hierarchy, and the $U(1)$ coset of the Polyakov-Bershadsky $\\cw$ algebra, leading to a $3$-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies.
Rationality, institutions and environmental policy
Vatn, Arild [Department of Economics and Resource Management, Norwegian University of Life Sciences, Aas (Norway)
2005-11-01
This paper is about how institutions determine choices and the importance of this for environmental policy. The model of individual rational choice from neoclassical economics is compared with the model of socially determined behavior. While in the first case, institutions are either exempted from or understood as mere economizing constraints on behavior, the latter perspective views institutions as basic structures necessary also to enable people to act. The paper develops a way to integrate the individualistic model into the wider perspective of social constructivism by viewing it as a special form of such construction. On the basis of this synthesis three issues with relevance for environmental economics are discussed. First, the role of institutional factors in the process of preference formation is emphasized. Next, the role of institutions for the choice of desired states of the environment is analyzed. Finally, the effect of various policy instruments to motivate people to produce these states is discussed. It is concluded that the core policy issue is to determine which institutional frameworks are most reasonable to apply to which kind of problem. Issues, which from the perspective of neoclassical economics are pure technical, become serious value questions if understood from an institutional perspective.
[RATIONAL ASPECTS OF BACTERIOPHAGES USE].
Vakarina, A A; Kataeva, L V; Karpukhina, N F
2015-01-01
Analysis of existing aspects of bacteriophage use and study features of their lytic activity by using various techniques. Effect of monophages and associated bacteriophages (staphylococci, piopolyvalent and piocombined, intestiphage, pneumonia klebsiella and polyvalent klebsiella produced by "Microgen") was studied with 380 strains of Staphylococcus aureus and 279 cultures of Klebsiella pneumoniae in liquid and solid nutrient media. From patients with intestinal disorder, sensitivity was analyzed to 184 strains of Salmonella genus bacteria 18 serological variants to salmonella bacteriophages, 137 strains of Escherichia coli (lactose-negative, hemolytic), as well as some members of OKA groups (21 serovars) to coli-proteic and piopolyvalent bacteriophages. Lytic ability of the piobacteriophage against Klebsiella and Proteus genus bacteria was determined. Staphylococcus aureus was sensitive to staphylococcus bacteriophage in 71.6% of cases and to piobacteriophage--in 86.15% of cases. A 100% lytic ability of salmonella bacteriophage against Salmonella spp. was established. Sensitivity of E. coli of various serogroups to coli-proteic and piobacteriophage was 66 - 100%. Klebsiella, Proteus genus bacteria were sensitive to piobacteriophage in only 35% and 43.15% of cases, respectively. A more rational use of bacteriophages is necessary: development of a technique, evaluation of sensitivity of bacteria to bacteriophage, introduction of corrections into their production (expansion of bacteriophage spectra, determination and indication of their concentration in accompanying documents).
Xu, Junyan
2012-01-01
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.
MOK; Ngaiming
2008-01-01
In 1993,Tsal proved that a proper holomorphic mapping f:Ω→Ω’ from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ’ is necessarily totally geodesic provided that r’:=rank(Ω’)≤rank(Ω):= r,proving a conjecture of the author’s motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents(VMRTs). In another completely different direction Hwang-Mok established with very few exceptions the Cartan- Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num- ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio- nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com- plex Grassmann manifolds of rank≤2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin’s which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures.
Points rationnels sur les quotients d'Atkin-Lehner de courbes de Shimura de discriminant $pq$
Gillibert, Florence
2010-01-01
Let $p$ and $q$ be two distinct prime numbers, and $X^{pq}/w_q$ be the quotient of the Shimura curve of discriminant $pq$ by the Atkin-Lehner involution $w_q$. We describe a way to verify in wide generality a criterion of Parent and Yafaev to prove that if $p$ and $q$ satisfy some explicite congruence conditions, known as the conditions of the non ramified case of Ogg, and if $p$ is large enough compared to $q$, then the quotient $X^{pq}/w_q$ has no rational point, except possibly special points.
Profit allocation among rational players in a cooperative game under uncertainty
Sibasis Bandyopadhyay; Swapan Raha; Prasun Kumar Nayak
2015-06-01
In this paper, a cooperative game has been considered, where there is a coalition between rational players in an uncertain environment. The uncertainty occurs in terms of the quality of the raw material. The pay-offs of the players are influenced by the degree of satisfaction. Pay-offs are considered as interval numbers. A multisection technique has been applied to obtain a rational solution. In the process, it has been found that the degree of satisfaction of the rational players converges to its optimum value with the convergence of the iterations. A comparative study has been made with methods existing in the literature.
Senior doctors' opinions of rational suicide.
Ginn, Stephen; Price, Annabel; Rayner, Lauren; Owen, Gareth S; Hayes, Richard D; Hotopf, Matthew; Lee, William
2011-12-01
The attitudes of medical professionals towards physician assisted dying have been widely discussed. Less explored is the level of agreement among physicians on the possibility of 'rational suicide'-a considered suicide act made by a sound mind and a precondition of assisted dying legislation. To assess attitudes towards rational suicide in a representative sample of senior doctors in England and Wales. A postal survey was conducted of 1000 consultants and general practitioners randomly selected from a commercially available database. The main outcome of interest was level of agreement with a statement about rational suicide. The corrected participation rate was 50%; 363 questionnaires were analysed. Overall 72% of doctors agreed with the possibility of rational suicide, 17% disagreed, and 11% were neutral. Doctors who identified themselves as being more religious were more likely to disagree. Some doctors who disagreed with legalisation of physician assisted suicide nevertheless agreed with the concept of rational suicide. Most senior doctors in England and Wales feel that rational suicide is possible. There was no association with specialty. Strong religious belief was associated with disagreement, although levels of agreement were still high in people reporting the strongest religious belief. Most doctors who were opposed to physician assisted suicide believed that rational suicide was possible, suggesting that some medical opposition is best explained by other factors such as concerns of assessment and protection of vulnerable patients.
MLODESTKY V. R.
2015-09-01
Full Text Available Statement of the problem. The main points of contractual obligations is their timely performance with ensuring the desired level of investments of the investment funds provided for in this contract. The longer the execution of the works under the contract, the higher the probability of violation of these terms. Analysis of construction projects over the past decade has shown that the situation has not changed significantly, according to [8] contemporary data on the construction of a number of objects from which it follows that the larger the object, and accordingly, the longer construction period, the more the actual deviation of the actual terms of the construction of the planned, up to 50...100% in some cases. The comparison of these data shows that the problem of ensuring reliable operation of the construction company on the stage of implementation of a specific project is relevant in the present time. Analysis of recent research. The analysis of researches in the field of the rational justification of organizational and technological reliability values shows that its range is in the range from 0.35 to 0.9, it indicates the absence of a reasoned approach to this issue. Of course, for a more reliable implementation of the plan one needs to have a certain amount of appropriate material and financial resources, but in the management process is another important resource that should be in possession of the subject of management this is information. The purpose and objectives of work. The aim of this work is the study of the rational level of organizational and technological reliability (OTR based on analysis of the need for this information. To achieve the goal of the article were set and solve the following tasks: - to establish the relationship between OTR and the right amount of information; - to determine the influence of the accuracy of determining the current state of the controlled parameter and the level of information; - to justify the
Rational Verification in Iterated Electric Boolean Games
Youssouf Oualhadj
2016-07-01
Full Text Available Electric boolean games are compact representations of games where the players have qualitative objectives described by LTL formulae and have limited resources. We study the complexity of several decision problems related to the analysis of rationality in electric boolean games with LTL objectives. In particular, we report that the problem of deciding whether a profile is a Nash equilibrium in an iterated electric boolean game is no harder than in iterated boolean games without resource bounds. We show that it is a PSPACE-complete problem. As a corollary, we obtain that both rational elimination and rational construction of Nash equilibria by a supervising authority are PSPACE-complete problems.
COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS
檀结庆
2003-01-01
As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.
Positivity Preserving Interpolation Using Rational Bicubic Spline
Samsul Ariffin Abdul Karim
2015-01-01
Full Text Available This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE, our partially blended rational bicubic spline is on a par with the established methods.
Bounded rational choice behaviour: applications in transport
Jensen, Anders Fjendbo
2016-01-01
rational choice behaviour focuses on how the latter approach can be seriously taken into account within transport applications. As the editors discuss in the introduction, a true optimal choice can only be made if an individual has full and perfect information of all relevant attributes in his/her choice......Even though the theory of rational behaviour has been challenged for almost 100 years, the dominant approach within the field of transport has been based upon the assumptions of neoclassical economics that we live in a world of rational decision makers who always have perfect knowledge and aim...
Comparable stocks, boundedly rational stock markets and IPO entry rates.
Jay Chok
Full Text Available In this study, we examine how initial public offerings (IPO entry rates are affected when stock markets are boundedly rational and IPO firms infer information from their counterparts in the market. We hypothesize a curvilinear relationship between the number of comparable stocks and initial public offerings (IPO entry rates into the NASDAQ Stock Exchange. Furthermore, we argue that trading volume and changes in stock returns partially mediates the relationship between the number of comparable stocks and IPO entry rates. The statistical evidence provides strong support for the hypotheses.
Rationing health care--should it be done?
Perrin, K
1989-09-01
1. The utilitarian view supports allocation of goods to meet the needs of the greatest number of people; Lamm contends that the only just rationing would be according to age. 2. Some theorists assume that all individuals will live relatively healthily until the end of their natural lifespan; they do not distinguish between therapeutic medications and those that alleviate suffering. 3. According to intergenerational arguments, children should receive priority in funding, with the elderly at the lower end of the scale. 4. The Advisory Panel of the Office of Technology Assessment recommends rationing based on prognosis and quality of life; however, good prognostic skills are lacking and there is no consensus on quality of life.
A General Theory of Computational Scalability Based on Rational Functions
Gunther, Neil J
2008-01-01
The universal scalability law (USL) of computational capacity is a rational function C_p = P(p)/Q(p) with P(p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has long been used for statistical modeling and prediction of computer system performance. We prove that C_p is equivalent to the synchronous throughput bound for a machine-repairman with state-dependent service rate. Simpler rational functions, such as Amdahl's law and Gustafson speedup, are corollaries of this queue-theoretic bound. C_p is both necessary and sufficient for modeling all practical characteristics of computational scalability.
Rational functions with maximal radius of absolute monotonicity
Loczi, Lajos
2014-05-19
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.
On rational solution of the state equation of a finite automaton
R. Chaudhuri
1988-01-01
Full Text Available We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.
Duan's fixed point theorem: Proof and generalization
Arkowitz Martin
2006-01-01
Full Text Available Let be an H-space of the homotopy type of a connected, finite CW-complex, any map and the th power map. Duan proved that has a fixed point if . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a -structure as defined by Hemmi-Morisugi-Ooshima. The conclusion is that and each has a fixed point.
Aanæs, Henrik; Dahl, Anders Lindbjerg; Pedersen, Kim Steenstrup
2012-01-01
on spatial invariance of interest points under changing acquisition parameters by measuring the spatial recall rate. The scope of this paper is to investigate the performance of a number of existing well-established interest point detection methods. Automatic performance evaluation of interest points is hard......Not all interest points are equally interesting. The most valuable interest points lead to optimal performance of the computer vision method in which they are employed. But a measure of this kind will be dependent on the chosen vision application. We propose a more general performance measure based...... position. The LED illumination provides the option for artificially relighting the scene from a range of light directions. This data set has given us the ability to systematically evaluate the performance of a number of interest point detectors. The highlights of the conclusions are that the fixed scale...
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
Beyond rationality : Counterfactual thinking and behavior regulation
Epstude, Kai; Roese, Neal J.
2007-01-01
Counterfactual thinking may be described as disciplined realistic, and rational, but we move a step further to describe a theoretical perspective centering on behavior regulation. According to this perspective, counterfactual thinking primarily centers on coordination of ongoing behavior. In short,
Environmental Management: the Ideology of Natural Resource Rational Use
Zolotukhin, V. M.; Gogolin, V. A.; Yazevich, M. Yu; Baumgarten, M. I.; Dyagileva, A. V.
2017-01-01
The article presents an analysis of the ontological and methodological principles of environmental management. These principles form the united ideology of natural resource rational use as the environment preservation basis. Consideration of environmental issues from the environmental management point of view is stipulated by the concern of the scientific community about the existence of mankind and the sphere of its inhabiting. The need to overcome the stereotypes existing in mass consciousness about safe and environmentally friendly consumption is stressed. The process of forming environmental management policy should contribute to the stabilization (balancing) of the consumers’ expectations and collective decision-making based on a public ecological consensus.
Is crime in Turkey economically rational?
2014-01-01
The study investigates whether crime in Turkey is governed by economic rationality. An economic model of rational behaviour claims that the propensity to commit criminal activities is negatively related to risk of deterrence. Potential presence of higher risk profiles for certain population segments is investigated. Panel data aggregated to sub-regional levels and observed annually for the years 2008 to 2010 are applied. Controls for endogeneity among criminal activity level and risk of deter...
Multinode rational operators for univariate interpolation
Dell'Accio, Francesco; Di Tommaso, Filomena; Hormann, Kai
2016-10-01
Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this talk we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant.
2-rational Cubic Spline Involving Tension Parameters
M Shrivastava; J Joseph
2000-08-01
In the present paper, 1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given monotonic data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a 2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
Is crime in Turkey economically rational?
Lauridsen, Jørgen T.; Zeren, Fatma; Ari, Ayse
2014-01-01
The study investigates whether crime in Turkey is governed by economic rationality. An economic model of rational behaviour claims that the propensity to commit criminal activities is negatively related to risk of deterrence. Potential presence of higher risk profiles for certain population segments is investigated. Panel data aggregated to sub-regional levels and observed annually for the years 2008 to 2010 are applied. Controls for endogeneity among criminal activity level and risk of deter...
Rational emotive behaviour therapy: distinctive features
Dryden, Windy
2008-01-01
Rational emotive behaviour therapy (REBT) encourages the client to focus on their emotional problems in order to understand, challenge and change the irrational beliefs that underpin these problems. REBT can help clients to strengthen conviction in their alternative rational beliefs by acting in ways that are consistent with them and thus encourage a healthier outlook.\\ud \\ud This accessible and direct guide introduces the reader to REBT while indicating how it is different from other approac...
Artificial intelligence techniques for rational decision making
Marwala, Tshilidzi
2014-01-01
Develops insights into solving complex problems in engineering, biomedical sciences, social science and economics based on artificial intelligence. Some of the problems studied are in interstate conflict, credit scoring, breast cancer diagnosis, condition monitoring, wine testing, image processing and optical character recognition. The author discusses and applies the concept of flexibly-bounded rationality which prescribes that the bounds in Nobel Laureate Herbert Simon's bounded rationality theory are flexible due to advanced signal processing techniques, Moore's Law and artificial intellig
The neural basis of bounded rational behavior
Coricelli, Giorgio; Nagel, Rosemarie
2010-01-01
Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting —the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. ...
Integral Models of Extremal Rational Elliptic Surfaces
Jarvis, Tyler J; Ricks, Jeremy R
2009-01-01
Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson's classification has an integral model with good reduction everywhere (except for those of type X_{11}(j), which is an exceptional case), and that every extremal rational elliptic surface over an algebraically closed field of characteristic p > 0 can be obtained by reducing one of these integral models mod p.
Rational emotive behavior therapy: disputing irrational philosophies.
Sacks, Susan Bendersky
2004-05-01
This article provides an overview of the concepts and techniques of rational emotive behavior therapy to distinguish it from cognitive-behavioral therapy. Rational emotive behavior therapy proposes that psychological disturbance is largely created and maintained through irrational philosophies consisting of internal absolutistic demands. This therapy strives to produce sustained and profound cognitive, emotive, and behavioral change through active, vigorous disputation of underlying irrational philosophies.
Municipal management cooperation : managing multiple rationalities
Holmberg, Leif
2010-01-01
Multiple rationality organizations are characterized by the simultaneously incorporation of different kinds of logic and control systems. They have to provide not only for efficiency but also to comply with e.g. ideal of fairness, sportsmanship, equal rights, and aesthetic values. Elite sport clubs, theatres, and several municipality activities are examples of organizations that have to cope with multiple rationalities. These organizations are often governed through a combination of politica...
Précis of bayesian rationality: The probabilistic approach to human reasoning.
Oaksford, Mike; Chater, Nick
2009-02-01
According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic--the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. Bayesian Rationality argues that rationality is defined instead by the ability to reason about uncertainty. Although people are typically poor at numerical reasoning about probability, human thought is sensitive to subtle patterns of qualitative Bayesian, probabilistic reasoning. In Chapters 1-4 of Bayesian Rationality (Oaksford & Chater 2007), the case is made that cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems. In Chapters 5-7 the psychology of "deductive" reasoning is tackled head-on: It is argued that purportedly "logical" reasoning problems, revealing apparently irrational behaviour, are better understood from a probabilistic point of view. Data from conditional reasoning, Wason's selection task, and syllogistic inference are captured by recasting these problems probabilistically. The probabilistic approach makes a variety of novel predictions which have been experimentally confirmed. The book considers the implications of this work, and the wider "probabilistic turn" in cognitive science and artificial intelligence, for understanding human rationality.
Changing fields of rationality - a policy for change?
Strumse, Einar; Westskog, Hege; Winther, Tanja
2010-07-01
Work objective: To analyze effective strategies for changing households' energy consumption based on an interdisciplinary model for understanding change. Methodology: In this paper we develop a conceptual model for understanding individuals' energy consumption. We synthesize insights from anthropology, social psychology and economics grasping perspectives from behaviour to practice and from the Bourdieu's fields to rationality thinking in economics. We use this insight to analyze strategies for change. Abstract: In this paper we analyze effective strategies for changing households' energy consumption based on an interdisciplinary model for understanding change. The model focuses on four main categories for understanding individual consumption: a. Material constraints b. Values and identity c. Norms d. Ability These are the main influencing factors of the individual's consumption level, but in interaction with the corresponding group and the societal levels for the same factors. The model can be illustrated. One combination of factors on all levels constitutes a field of rationality. We claim that an important strategy for changing energy consumption towards sustainability is changing the field of rationality of the individual. Changing of rationality fields would from our point of view initiate reflection which is an important condition for changed behavior. One example of changing of fields is information measures that relates energy consumption to the 'citizen' field rather than the 'consumer' field. Hence, according to our conceptual framework - how policy should be framed (information measures for instance ) would be an important knowledge area for design of effective policy measures. (Author)
Serial floating point formatter
Peterson, R. D.; Penner, W. A.
1985-11-12
A floating point formatter for changing fixed point serial digital data, such as that received by a seismic data acquisition system, is disclosed wherein fixed point serial digital data is received and scaled to remove any bias added by preamplification. The scaled data is shifted a predetermined number of bits and a resulting exponent is calculated. The shifted data signal and corresponding exponent are combined and further scaled to permit stacking the data without exceeding the system capacity.
Intergroup conflict and rational decision making.
Vicente Martínez-Tur
Full Text Available The literature has been relatively silent about post-conflict processes. However, understanding the way humans deal with post-conflict situations is a challenge in our societies. With this in mind, we focus the present study on the rationality of cooperative decision making after an intergroup conflict, i.e., the extent to which groups take advantage of post-conflict situations to obtain benefits from collaborating with the other group involved in the conflict. Based on dual-process theories of thinking and affect heuristic, we propose that intergroup conflict hinders the rationality of cooperative decision making. We also hypothesize that this rationality improves when groups are involved in an in-group deliberative discussion. Results of a laboratory experiment support the idea that intergroup conflict -associated with indicators of the activation of negative feelings (negative affect state and heart rate- has a negative effect on the aforementioned rationality over time and on both group and individual decision making. Although intergroup conflict leads to sub-optimal decision making, rationality improves when groups and individuals subjected to intergroup conflict make decisions after an in-group deliberative discussion. Additionally, the increased rationality of the group decision making after the deliberative discussion is transferred to subsequent individual decision making.
Intergroup conflict and rational decision making.
Martínez-Tur, Vicente; Peñarroja, Vicente; Serrano, Miguel A; Hidalgo, Vanesa; Moliner, Carolina; Salvador, Alicia; Alacreu-Crespo, Adrián; Gracia, Esther; Molina, Agustín
2014-01-01
The literature has been relatively silent about post-conflict processes. However, understanding the way humans deal with post-conflict situations is a challenge in our societies. With this in mind, we focus the present study on the rationality of cooperative decision making after an intergroup conflict, i.e., the extent to which groups take advantage of post-conflict situations to obtain benefits from collaborating with the other group involved in the conflict. Based on dual-process theories of thinking and affect heuristic, we propose that intergroup conflict hinders the rationality of cooperative decision making. We also hypothesize that this rationality improves when groups are involved in an in-group deliberative discussion. Results of a laboratory experiment support the idea that intergroup conflict -associated with indicators of the activation of negative feelings (negative affect state and heart rate)- has a negative effect on the aforementioned rationality over time and on both group and individual decision making. Although intergroup conflict leads to sub-optimal decision making, rationality improves when groups and individuals subjected to intergroup conflict make decisions after an in-group deliberative discussion. Additionally, the increased rationality of the group decision making after the deliberative discussion is transferred to subsequent individual decision making.
CAO Jun-Peng; HOU Bo-Yu; YUE Rui-Hong
2001-01-01
The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain. After the quantum determinant being well defined, the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Gaudin model are given. These results can be generalized to any number of constituting spins (SU( N) ).
无
2001-01-01
The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain.After the quantum determinant being well defined,the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Geudin model are given.These results can be generalized to any number of constituting spins (SU(N)).
Rationally Dealing with Test Anxiety.
Rogers, George W., Jr.
Test anxiety is a common problem manifested by many college students. The Testing and Psychological Services Center at Northern Kentucky University sees a number of such students each semester. The possible causes of test anxiety are frequently the illogical or unrealistic demands that some students place on themselves. The methods of treatment…
Market equilibria under procedural rationality
Anufriev, M.; Bottazzi, G.
2010-01-01
We analyze the endogenous price formation mechanism of a pure exchange economy with two assets, riskless and risky. The economy is populated by an arbitrarily large number of traders whose investment choices are described by means of generic smooth functions of past realizations. These choices can
A discussion of theoretical and practical rationality
Wahlstroem, B. [Technical Research Centre of Finland, Espoo (Finland). VTT Automation
1999-12-01
Theoretical rationality as defined in Expected Utility Theory and amended with other considerations gives a good basis for decision making. One should however always keep in mind that practical rationality often is far more complicated. People use their everyday experience when placed before new problems and this may lead to apparently irrational choices which on a closer scrutiny may be completely rational. Theories in human decision making unfortunately becomes untestable, firstly because a theory taking all considerations into account would be to complex to be practical and secondly because the data needed to test the theory cannot be collected. The benefit of EUT is that it is simple and straightforward as compared with competing theories. In the natural sciences rationality is often seen simply as a problem of optimisation. This view is practical, but it has to include also psychological and sociological considerations. The apparent controversy between natural and behavioural sciences could at least in principle be resolved by a better understanding of the complexity of human rationality. The human mind does not work in isolation, but it is adapted to a social community and a continuously changing environment. Understanding all components of human rationality is a challenge which cannot be solved on a short term basis. An important part of human rationality is connected to the intricate balance between individual and societal utility. The human mind has over thousands of years learnt to resolve that balance, but in the modern society there are decisions which may not be solvable with an intuitive approach and a strategy of trial and error. For these decisions more solid theories of rationality will be needed. EUT can in spite of its dismerits be used as the backbone for such a theory, but it has to be extended with better explanations of both individual and social rationality. If this understanding of the practical aspects of human rationality can be reached
Rational Design of Composite Panels
Riber, Hans Jørgen
1996-01-01
panels as well as single-skin panels, the effect of shear is included. The finite difference method is used solving the system of governing plate equations. Laterally loaded panels are analysed with respect to mid-point deflections and stresses. The numerical results are discussed in the light of 'Det......A non-linear structural model for composite panels is presented. The non-linear terms in the lateral displacements are modelled as an additional set of lateral loads acting on the panel. Hence the solution is reduced to that of an equivalent panel with small displacements In order to treat sandwich...
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New series of odd non-congruent numbers
FENG; Keqin
2006-01-01
We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and (S)n of the elliptic curve En: y2 = x(x - n)(x - 2n) and its dual curve (E)n: y2 =x3 + 6nx2 + n2x have the smallest size: Sn = {1}, (S)n = {1, 2, n, 2n}. It is well known that for such integer n, the rank of group En(Q) of the rational points on En is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves En with rank zero and such series of integers n are non-congruent numbers.
Verifiable Rational Secret Sharing Scheme in Mobile Networks
En Zhang
2015-01-01
Full Text Available With the development of mobile network, lots of people now have access to mobile phones and the mobile networks give users ubiquitous connectivity. However, smart phones and tablets are poor in computational resources such as memory size, processor speed, and disk capacity. So far, all existing rational secret sharing schemes cannot be suitable for mobile networks. In this paper, we propose a verifiable rational secret sharing scheme in mobile networks. The scheme provides a noninteractively verifiable proof for the correctness of participants’ share and handshake protocol is not necessary; there is no need for certificate generation, propagation, and storage in the scheme, which is more suitable for devices with limited size and processing power; in the scheme, every participant uses her encryption on number of each round as the secret share and the dealer does not have to distribute any secret share; every participant cannot gain more by deviating the protocol, so rational participant has an incentive to abide by the protocol; finally, every participant can obtain the secret fairly (means that either everyone receives the secret, or else no one does in mobile networks. The scheme is coalition-resilient and the security of our scheme relies on a computational assumption.
Dynamic pricing of network goods with boundedly rational consumers.
Radner, Roy; Radunskaya, Ami; Sundararajan, Arun
2014-01-07
We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational and unable either to pay immediate attention to each price change or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller's optimal price trajectory has the following structure: The price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep the user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product's user base evolving over time and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium and are more consistent with the pricing of network goods observed in practice.
From Whole Numbers to Invert and Multiply
Cavey, Laurie O.; Kinzel, Margaret T.
2014-01-01
Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…
Ufnarovski, Victor; Ahlander, Bo
2003-09-01
We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.
Mendonça, J. Ricardo G.
2012-01-01
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.
Cosmin Toth
2013-06-01
Full Text Available Some of the most known and fertile models for understanding human behaviour are those which rest on the assumption of human rationality. These models have specific strategies for dealing with situations in which understanding human behaviour becomes difficult, i.e. cases of irrationality, and this, in turn, leads to particular methodological consequences. The aim of this article is to illustrate and systematize some of the typical theoretical approaches to the issues of rationality and irrationality and their methodological consequences, while warning, at the same time, against the risks of applying rationality models of a pronounced normative-evaluative nature. A number of important methodological consequences of applying the principle of charity to various degrees of strength are analysed and a taxonomic grid for the different ways of approaching rationality is presented.
Kneusel, Ronald T
2015-01-01
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb
Number names and number understanding
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
through using mathematical names for the numbers such as one-ten-one for 11 and five-ten-six for 56. The project combines the renaming of numbers with supporting the teaching with the new number names. Our hypothesis is that Danish children have more difficulties learning and working with numbers, because...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....
On computing closed forms for summations. [polynomials and rational functions
Moenck, R.
1977-01-01
The problem of finding closed forms for a summation involving polynomials and rational functions is considered. A method closely related to Hermite's method for integration of rational functions derived. The method expresses the sum of a rational function as a rational function part and a transcendental part involving derivatives of the gamma function.
Using Rational-Emotive Therapy to Prevent Classroom Problems.
Webber, Jo; Coleman, Maggie
1988-01-01
Teachers are encouraged to utilize rational-emotive therapy to prevent and deal with classroom behavior problems. Rational-emotive therapy is defined, the ABC model of rational thinking briefly explained, types of irrational thinking identified, and suggestions for becoming a rational thinker are offered. Classroom examples are given. (DB)
The database search problem: a question of rational decision making.
Gittelson, S; Biedermann, A; Bozza, S; Taroni, F
2012-10-10
This paper applies probability and decision theory in the graphical interface of an influence diagram to study the formal requirements of rationality which justify the individualization of a person found through a database search. The decision-theoretic part of the analysis studies the parameters that a rational decision maker would use to individualize the selected person. The modeling part (in the form of an influence diagram) clarifies the relationships between this decision and the ingredients that make up the database search problem, i.e., the results of the database search and the different pairs of propositions describing whether an individual is at the source of the crime stain. These analyses evaluate the desirability associated with the decision of 'individualizing' (and 'not individualizing'). They point out that this decision is a function of (i) the probability that the individual in question is, in fact, at the source of the crime stain (i.e., the state of nature), and (ii) the decision maker's preferences among the possible consequences of the decision (i.e., the decision maker's loss function). We discuss the relevance and argumentative implications of these insights with respect to recent comments in specialized literature, which suggest points of view that are opposed to the results of our study.
Rational drug design applied to myeloperoxidase inhibition.
Van Antwerpen, P; Zouaoui Boudjeltia, K
2015-06-01
Rational drug design is a general approach using protein-structure technique in which the discovery of a ligand can be driven either by chance, screening, or rational theory. Myeloperoxidase (MPO) was rapidly identified as a therapeutical target because of its involvement in chronic inflammatory syndromes. In this context, the research of MPO inhibitors was intensified and development of new chemical entities was rationally driven by the research of ligands that enter into the MPO catalytic pocket. Actually, as soon as crystallography data of MPO have become available and its structure was virtually designed, the rational drug design has been applied to this peroxidase. Pharmaceutical industries and academic laboratories apply rational drug design on MPO by either optimizing known inhibitors or searching new molecules by high-throughput virtual screening. By these ways, they were able to find efficient MPO inhibitors and understand their interactions with the enzyme. During this quest of MPO inhibition, it appears that Glu268 is a crucial residue in order to optimize ligand-target interaction. This amino acid should be carefully considered by medicinal chemist when they design inhibitors interfering with MPO activity.
Dynamic Evaluation of Rationality of Land Use Structure in the Changsha-Zhuzhou-Xiangtan Area
Jinning XIE; Jianhua GUO; Kaiguo YUAN; Bin QUAN
2015-01-01
The rationality of land use structure was evaluated with dynamic TOPSIS method based on changing data of land use from 2008 to 2011 in the Changsha-Zhuzhou-Xiangtan area. The results showed that during 2008- 2011,the rationality of land use structure was totally high,the dynamic value hi of Changsha,Zhuzhou,Xiangtan and the Changsha-Zhuzhou-Xiangtan area was 0. 7954,0. 7821,0. 8245 and0. 8186,respectively; the value Ci( tk) reflecting the rationality of land use structure at different time points was rapidly increased,and the gap between regions was not big and shrinking. According to the grey relational analysis,the change of different land use types had different effects on the rationality of land use structure: transportation land,the land for cities,towns and villages and the land for mining and industry are most highly correlated with the rationality of land use structure,while arable land,woodland,water area and water conservancy facility land have also an important impact on the rationality of land use structure; controlling the excessive growth of transportation land,the land for cities,towns and villages and the land for mining and industry,protecting arable land,forest land,water area and water conservancy facility land,and moderately increasing the garden plot,plays a decisive role in optimizing the land use structure in the Changsha-Zhuzhou-Xiangtan area.
Full Text Available ... Point by CPSC Blogger September 22, 2009 appliance child Childproofing CPSC danger death electrical fall furniture head ... see news reports about horrible accidents involving young children and furniture, appliance and tv tip-overs. The ...
Oligopolistic Banks, Bounded Rationality, and the Credit Cycle
Tobias F. Rötheli
2012-01-01
Full Text Available This paper studies how boundedly rational default expectations affect the credit cycle. I propose a simple model of oligopolistic bank competition which serves to compare situations with just a portion of boundedly rational banks to situations where either all banks are rational or all banks are boundedly rational. When all banks are boundedly rational, the credit cycle is most amplified relative to the situation where all banks are rational. However, the amplifying effect of bounded rationality on the side of banks largely remains even when only a portion of banks are boundedly rational. Hence, the interest rate decisions of a minority of boundedly rational banks induce the more rational competitors to aggravate the credit cycle.
IDENTITIES INVOLVING RATIONAL SUMS BY INVERSION AND PARTIAL FRACTION DECOMPOSITION
Helmut Prodinger
2008-03-01
Full Text Available Identities appearing recentlyin: {sc J. L. D'{i}az-Barrero, J. Gibergans-B'agu-ena, P. G. Popescu:}{it Some identities involving rational sums}. Appl. Anal. Discrete Math., {f 1} (2007, 397--402, aretreated by inverting them; the resulting sums areevaluated using partial fraction decomposition, following{sc Wenchang Chu:} {it A binomial coefficient identity associated with {B}eukers' conjectureon {A}p'ery numbers.} Electron. J. Combin., {f 11} (1: Note 15, 3 pp. (electronic, 2004.This approach produces a general formula, not only special cases.
RATIONAL STEEL CORRUGATED PROFILE DESIGN
V. V. Kachurenko
2015-08-01
Full Text Available Purpose. The work sets forth the search results of new, more efficient design solutions for metal silos, namely, the analysis of existing types of profiles cross-section in a steel wall of such silo and development of less material-intensive section of corrugated profile.Methodology. To achieve the set goal there were researched the existing types of capacitive structure profiles and their strain-stress state under the load. The analysis was performed on the results of computational experiments. The prototype object was mathematical computer models. The calculations were made using the finite-element method. For computational experiment there was used the design-computing system Structure CAD for Windows. Findings. In this work there were obtained the data allowing to assess work of the profiles and to find more effective type of cross-section in terms of its material consumption. In the process of joint study of the authors a new type of profile for capacitive structures was developed; it has higher utilization efficiency and the attachment point of individual steel sheets with this type of profile. Both solutions are easy to install, reliable in operation and can be manufactured in the conditions of modern industrial production using standard equipment, materials and components. Originality. A new type of corrugated profile cross-section for steel silo walls was proposed; it has higher load carrying capacity and rigidity and allows reducing the metal thickness without changing the structure carrying capacity that results in material consumption reduction of the whole structure.For this and similar types of profiles there was designed and proposed the attachment point of individual corrugated sheets screwed with extending flange, which enables the unit connection in case of small size corrugations, where the distance is not sufficient to accommodate the bolt cap between the individual corrugations. Practical value.Application of the proposed
Changing Conspiracy Beliefs through Rationality and Ridiculing
Gábor Orosz
2016-10-01
Full Text Available Conspiracy theory (CT beliefs can be harmful. How is it possible to reduce them effectively? Three reduction strategies were tested in an online experiment using general and well-known CT beliefs on a comprehensive randomly assigned Hungarian sample (N = 813: exposing rational counter CT arguments, ridiculing those who hold CT beliefs, and empathizing with the targets of CT beliefs. Several relevant individual differences were measured. Rational and ridiculing arguments were effective in reducing CT, whereas empathizing with the targets of CTs had no effect. Individual differences played no role in CT reduction, but the perceived intelligence and competence of the individual who conveyed the CT belief-reduction information contributed to the success of the CT belief reduction. Rational arguments targeting the link between the object of belief and its characteristics appear to be an effective tool in fighting conspiracy theory beliefs.
Rational speculative bubbles: A critical view
Radonjić Ognjen
2007-01-01
Full Text Available According to the theory of rational bubbles, the bubble is present whenever asset prices progressively diverge from their fundamental value, which occurs because agents expect that asset prices will continue to grow exponentially (self-fulfilling prophecies far in the future and consistently, which promises the realization of ever larger capital gains. In our opinion, the basic shortcoming of this theory refers to the assumption that all market agents are perfectly informed and rational and, accordingly, form homogeneous expectations. The model does not explain decision-making processes or expectation formation, nor does it detect potential psychological and institutional factors that might significantly influence decision making processes and market participants’ reactions to news. Since assumptions of the model critically determine its validity, we conclude that comprehensiveness of the rational bubble model is, to put it mildly, limited.
Direct Extraction of One Loop Rational Terms
Badger, S D
2009-01-01
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. Working in D=4-2*epsilon dimensions, we interpret the dependence on the additional dimensions as equivalent to introducing an internal mass. We combine this with the use of generalised unitarity to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in 4-2*epsilon dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted analytically or numerically using discrete Fourier projections. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs.
Menzel, Paul T
1992-04-01
[In his review essay in this issue of Bioethics,] Julian Savulescu lucidly summarizes and assesses each essay in Strong Medicine. I would like to clarify a few important general points about prior consent as a conceptual framework for the ethical rationing of health care, correct several specific misreadings, and defend my basic claim despite some acknowledged problems.
Dainora Grundey
2008-01-01
The purpose of this paper is to show peculiarities of traditional and experiential marketing and describe why experiential marketing is better way to understand consumer behaviour. Comparative analysis shows the main characteristics of traditional and experiential marketing. Traditional marketing characteristics are there: product functional characteristics and superiority, narrow determinate product categories, point of view to the consumer as a rational thinker, application analytical, quan...
Space cutter compensation method for five-axis nonuniform rational basis spline machining
Yanyu Ding
2015-07-01
Full Text Available In view of the good machining performance of traditional three-axis nonuniform rational basis spline interpolation and the space cutter compensation issue in multi-axis machining, this article presents a triple nonuniform rational basis spline five-axis interpolation method, which uses three nonuniform rational basis spline curves to describe cutter center location, cutter axis vector, and cutter contact point trajectory, respectively. The relative position of the cutter and workpiece is calculated under the workpiece coordinate system, and the cutter machining trajectory can be described precisely and smoothly using this method. The three nonuniform rational basis spline curves are transformed into a 12-dimentional Bézier curve to carry out discretization during the discrete process. With the cutter contact point trajectory as the precision control condition, the discretization is fast. As for different cutters and corners, the complete description method of space cutter compensation vector is presented in this article. Finally, the five-axis nonuniform rational basis spline machining method is further verified in a two-turntable five-axis machine.
Does the Minimum Wage Cause Inefficient Rationing?
何满辉; 梁明秋
2008-01-01
By not allowing wages to dearthe labor market,the minimum wage could cause workers with low reservation wages to be rationed out while equally skilled woTkers with higher reservation wages are employed.I find that proxies for reservation wages of unskilled workers in high-impact stales did not rise relative to reservation wages in other states,suggesting that the increase in the minimum wage did not cause jobs to be allocated less efficiently.However,even if rationing is efficient,the minimum wage can still entail other efficiency costs.
[The role of economics in fair rationing].
Prenzler, A
2012-10-01
For several years academic disciplines have discussed the potential conflict between scarcity of funding and fair health care. This review article shows the necessity of involving economic scientists in this discussion as well as their contribution to rationalisation, prioritisation and rationing of health care services. Thereby, it becomes clear that rationing and justice are not a contradiction per se. The interdisciplinary discussion in Germany needs less disciplinary egotism and more willingness to seek solutions and compromises. In this context the procedures followed in other countries can serve as examples.
Medicinal cannabis: rational guidelines for dosing.
Carter, Gregory T; Weydt, Patrick; Kyashna-Tocha, Muraco; Abrams, Donald I
2004-05-01
The medicinal value of cannabis (marijuana) is well documented in the medical literature. Cannabinoids, the active ingredients in cannabis, have many distinct pharmacological properties. These include analgesic, anti-emetic, anti-oxidative, neuroprotective and anti-inflammatory activity, as well as modulation of glial cells and tumor growth regulation. Concurrent with all these advances in the understanding of the physiological and pharmacological mechanisms of cannabis, there is a strong need for developing rational guidelines for dosing. This paper will review the known chemistry and pharmacology of cannabis and, on that basis, discuss rational guidelines for dosing.
Topological Field Theory and Rational Curves
Aspinwall, Paul S; Aspinwall, Paul S.; Morrison, David R.
1993-01-01
We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by Candelas, de la Ossa, Green and Parkes.
Rationalization with ruled surfaces in architecture
Steenstrup, Kasper Hornbak
This thesis addresses the problems of rationalizing and segmenting large scale 3D models, and how to handle difficult production constraints in this area. The design choices when constructing large scale architecture are influenced by the budget. Therefore I strive to minimize the amount of time...... and material needed for production. This makes advanced free form architecture viable for low cost projects, allowing the architects to realize their designs. By pre-cutting building blocks using hot wire robots, the amount of milling necessary can be reduced drastically. I do this by rationalizing...
Rationality: A Social-Epistemology Perspective
Sylvia eWenmackers
2014-06-01
Full Text Available Both in philosophy and in psychology, human rationality has traditionally been studied from an 'individualistic' perspective. Recently, social epistemologists have drawn attention to the fact that epistemic interactions among agents also give rise to important questions concerning rationality. In previous work, we have used a formal model to assess the risk that a particular type of social-epistemic interactions lead agents with initially consistent belief states into inconsistent belief states. Here, we continue this work by investigating the dynamics to which these interactions may give rise in the population as a whole.
The Rational Hybrid Monte Carlo Algorithm
Clark, M A
2006-01-01
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
The Rational Hybrid Monte Carlo algorithm
Clark, Michael
2006-12-01
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
Rational design of protein kinase inhibitors
Yarmoluk S. M.
2013-07-01
Full Text Available Modern methodological approaches to rational design of low molecular weight compounds with specific activity in relation to predetermined biomolecular targets are considered by example of development of high effective protein kinase inhibitors. The application of new computational methods that allow to significantly improve the quality of computational experiments (in, particular, accuracy of low molecular weight compounds activity prediction without increase of computational and time costs are highlighted. The effectiveness of strategy of rational design is demonstrated by examples of several own investigations devoted to development of new inhibitors that are high effective and selective towards protein kinases CK2, FGFR1 and ASK1.
Rational homotopy theory and differential forms
Griffiths, Phillip
2013-01-01
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham's theorem on simplicial complexes. In addition, Sullivan's results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma*Presentation of a natu
Planas Vilà, Mercedes
2014-01-01
The current economic situation is the reason for this conference that will be split in two main areas: first, we will focus on general concepts on rationalizing versus rationing in health care, and secondly, on rationing in the practice of clinical nutrition. According to the Spanish Royal Academy of the Language, to rationalize is to organize the production or the work in a manner such the yields are increased or the costs are reduced with the least effort. However, to ration is the action and effect of rationing or limiting the consumption of something to prevent negative consequences. In Europe, the percentage of the Gross National Product dedicated to health care progressively decreases whereas the costs of health care are ever increasing. From the economic viewpoint, this would be the main reason why the health care authorities have no other option but rationing. Until what extent the ethical principle of justice is compatible with rationing? Ethically, it seems that in order to accept rationing, not only a fair distribution of the limited resources should be achieved, but also a rational use of them. If we accept that limiting the health care allowances is necessary, we should then answer some questions: is it ethical not to limit? Who decides what is medically necessary? How is it decided? With no coherent answers to these questions it is ethically difficult to accept rationing from a healthcare viewpoint. When dealing with rationing in the practice of clinical nutrition, we should focus on how rationing impacts on hyponutrition, and more particularly on disease-related hyponutrition, since this is the focus of Clinical Nutrition. Given its importance and its implications, in several countries, including Spain, actions integrated in the European Union strategy "Together for health: a Strategic Approach for the EU 2008-2013", are being performed aimed at taking decisions for preventing and managing hyponutrition. However, restrictions persist with the
E. H. Doha
2014-01-01
Full Text Available A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.
Rational design of modular circuits for gene transcription: A test of the bottom-up approach
Giordano Emanuele
2010-11-01
Full Text Available Abstract Background Most of synthetic circuits developed so far have been designed by an ad hoc approach, using a small number of components (i.e. LacI, TetR and a trial and error strategy. We are at the point where an increasing number of modular, inter-changeable and well-characterized components is needed to expand the construction of synthetic devices and to allow a rational approach to the design. Results We used interchangeable modular biological parts to create a set of novel synthetic devices for controlling gene transcription, and we developed a mathematical model of the modular circuits. Model parameters were identified by experimental measurements from a subset of modular combinations. The model revealed an unexpected feature of the lactose repressor system, i.e. a residual binding affinity for the operator site by induced lactose repressor molecules. Once this residual affinity was taken into account, the model properly reproduced the experimental data from the training set. The parameters identified in the training set allowed the prediction of the behavior of networks not included in the identification procedure. Conclusions This study provides new quantitative evidences that the use of independent and well-characterized biological parts and mathematical modeling, what is called a bottom-up approach to the construction of gene networks, can allow the design of new and different devices re-using the same modular parts.
Points of Low Degree on Smooth Plane Curves
Debarre, O; Debarre, Olivier; Klassen, Matthew
1992-01-01
The purpose of this note is to provide some applications of Faltings' recent proof of S. Lang's conjecture to smooth plane curves. Let $C$ be a smooth plane curve defined by an equation of degree $d$ with integral coefficients. We show that for $d\\ge 7$, the curve $C$ has only finitely many points whose field of definition has degree $\\le d-2$ over $Q$, and that for $d\\ge 8$, all but finitely many points of $C$ whose field of definition has degree $\\le d-1$ over $Q$ arise as points of intersection of rational lines through rational points of $C$.
无
2004-01-01
THE last digit of my home phone number in Beijing is 4. “So what?” European readers might ask.This was my attitude when I first lived in China; I couldn't understand why Chinese friends were so shocked at my indifference to the number 4. But China brings new discoveries every day, and I have since seen the light. I know now that Chinese people have their own ways of preserving their well being, and that they see avoiding the number 4 as a good way to stay safe.
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Ana Paula Ribeiro Bonilauri Ferreira
Full Text Available BACKGROUND: Little is known about the reasoning mechanisms used by physicians in decision-making and how this compares to diagnostic clinical practice guidelines. We explored the clinical reasoning process in a real life environment. METHOD: This is a qualitative study evaluating transcriptions of sixteen physicians' reasoning during appointments with patients, clinical discussions between specialists, and personal interviews with physicians affiliated to a hospital in Brazil. RESULTS: FOUR MAIN THEMES WERE IDENTIFIED: simple and robust heuristics, extensive use of social environment rationality, attempts to prove diagnostic and therapeutic hypothesis while refuting potential contradictions using positive test strategy, and reaching the saturation point. Physicians constantly attempted to prove their initial hypothesis while trying to refute any contradictions. While social environment rationality was the main factor in the determination of all steps of the clinical reasoning process, factors such as referral letters and number of contradictions associated with the initial hypothesis had influence on physicians' confidence and determination of the threshold to reach a final decision. DISCUSSION: Physicians rely on simple heuristics associated with environmental factors. This model allows for robustness, simplicity, and cognitive energy saving. Since this model does not fit into current diagnostic clinical practice guidelines, we make some propositions to help its integration.
Hirst, Keith
1994-01-01
Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc
Barnes, John
2016-01-01
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We gi
MINIMAL RATIONAL INTERPOLATION AND PRONYS METHOD
ANTOULAS, AC; WILLEMS, JC
1990-01-01
A new method is proposed for dealing with the rational interpolation problem. It is based on the reachability of an appropriately defined pair of matrices. This method permits a complete clarification of several issues raised, but not answered, by the so-called Prony method of fitting a linear model
Rational bargaining in games with coalitional externalities
Borm, Peter; Ju, Y.; Wettstein, D.
This paper provides a flexible strategic framework to analyze bargaining and values in environments with coalitional externalities. Within this framework we propose a new value that extends the Shapley value to partition function form games, the so-called Rational Belief Shapley (RBS) value. We
Rational Rhymes for Addressing Common Childhood Issues
Warren, Jeffrey M.
2011-01-01
Music-based interventions are valuable tools counselors can use when working with children. Specific types of music-based interventions, such as songs or rhymes, can be especially pertinent in addressing the thoughts, feelings, and behaviors of children. Rational-emotive behavior therapy (REBT) provides a therapeutic framework that encourages…
Dr. Strangelove and Irrational Collective Rationality
韩蕾
2012-01-01
Dr. Strangelove or: How I learned to Stop Worrying and Love the Bomb is a 1964 black comedy film with satire of arm races and nuclear scare by the director Stanley Kubrick. In the movie, irrational practice and ideologies manifest them⁃selves as collective rationality and result in the destruction of the earth.
Hietarinta, Jarmo; Hietarinta, Jarmo; Kajiwara, Kenji
1997-01-01
We study the rational solutions of the discrete version of Painleve's fourth equation d-PIV. The solutions are generated by applying Schlesinger transformations on the seed solutions -2z and -1/z. After studying the structure of these solutions we are able to write them in a determinantal form that includes an interesting parameter shift that vanishes in the continuous limit.
Bounded Rationality of Generalized Abstract Fuzzy Economies
Lei Wang
2014-01-01
Full Text Available By using a nonlinear scalarization technique, the bounded rationality model M for generalized abstract fuzzy economies in finite continuous spaces is established. Furthermore, by using the model M, some new theorems for structural stability and robustness to (λ,ϵ-equilibria of generalized abstract fuzzy economies are proved.
Rational Voters in a Partisanship Model
O.H. Swank (Otto)
1995-01-01
textabstractThis paper examines a voter model for the US which is interconnected with the partisan theory. In our model, voters are rational and forward-looking. They are perfectly informed about the preferences of political parties and about the state of the economy. The predictions of our voter mo
CONSTRAINED RATIONAL CUBIC SPLINE AND ITS APPLICATION
Qi Duan; Huan-ling Zhang; Xiang Lai; Nan Xie; Fu-hua (Frank) Cheng
2001-01-01
In this paper, a kind of rational cubic interpolation functionwith linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivative of the interpolating function is studied by using this interpolation, and as the consequent result, the convex interpolation conditions have been derived.
Robust identification for rational fractional transfer functions
王书宁
1997-01-01
An algorithm is proposed for robust identification of a rational fractional transfer function with a fixed degree under the framework of worst-case/deterministic robust identification. The convergence of the algorithm is proven. Its feasibility is shown with a numerical example.
Heterogeneous Parking Market Subject to Parking Rationing
Saeed Asadi Bagloee
2015-01-01
Full Text Available Different types of drivers and parking spaces delineate a heterogeneous parking market for which the literature has yet to provide a model applicable to the real world. The main obstacle is computational complexities of considering various parking restrictions along with traffic congestion on the road network. In this study, the heterogeneity aspects are considered within a Logit parking choice model. A mathematical programming problem was introduced to explicitly consider parking capacities and parking rationing constraints. The parking rationing is defined as any arrangement to reserve parking space for some specific demand such as parking permit, private parking, VIP parking, and different parking durations. Introduction of parking rationing in the presence of other constraints is a unique factor in this study which makes the model more realistic. The algorithm was tested on a central business district case study. The results prove that the algorithm is able to converge rapidly. Among the algorithm’s output are shadow prices of the parking capacity and parking rationing constraints. The shadow prices contain important information which is key to addressing a variety of parking issues, such as the location of parking shortages, identification of fair parking charges, viability of parking permits, and the size of reserved parking.
Multiple Equilibria in Noisy Rational Expectations Economies
Palvolgyi, Domotor; Venter, Gyuri
This paper studies equilibrium uniqueness in standard noisy rational expectations economies with asymmetric or differential information a la Grossman and Stiglitz (1980) and Hellwig (1980). We show that the standard linear equilibrium of Grossman and Stiglitz (1980) is the unique equilibrium...
The Rational Optimist: How Prosperity Evolves
Matt Ridley
2012-05-01
Full Text Available There is much debate about the state of the world. Matt Ridley argues in The Rational Optimist that we can solve problems such as economic crashes,population explosions, climate change and terrorism, of poverty, AIDS, depression and obesity. His trust of capitalism and progress is examined and challenged in this book review.
An Appraisal of Rational-Emotive Therapy.
Haaga, David A. F.; Davison, Gerald C.
1993-01-01
Scrutinizes rational-emotive therapy (RET) on conceptual and empirical grounds, including its reliance on constructive assessment and ethical stance. Notes that, although metanalytic reviews provide support for general utility of RET, more qualitative reviews question internal and external validity of much of published research. Notes that process…
Rational Emotive Behavior Therapy with Troubled Students.
Zionts, Paul; Zionts, Laura
1997-01-01
Based on the early work of Albert Ellis, seeks to identify and challenge irrational beliefs that underlie behavior problems. Outlines concepts and methods of Rational Emotive Behavior Theory and describes the application both in counseling and as a mental health curriculum for troubled children and youth. Offers classroom techniques. (RJM)
The Rational-Emotive Approach: A Critique
Morris, G. Barry
1976-01-01
The critique of Rational-Emotive Therapy aims criticism at Ellis' concept of irrationality, analysis of human behavior and therapeutic techniques. Ellis suggests that his critic's claims lack the support of experimental evidence. He further suggests that an "existential" bias pervades which differs from his own brand of "existentialism." (KRP)
Reflections on Rational-Emotive Therapy.
Ellis, Albert
1993-01-01
Reflects rational-emotive therapy (RET) in 1955 and discusses some of its recent constructivist and humanist theories and practice. Distinguishes between general RET, called synonymous with general cognitive-behavioral therapy, from preferential RET, called unique kind of cognitive therapy that partially overlaps with general cognitive-behavioral…
Rational Suggestions for Pre-Marital Counseling.
Ball, J.D.; Henning, Lawrence H.
1981-01-01
To demonstrate the utility of Rational Emotive Therapy in pre-marital counseling, examples of specific irrational beliefs which clinicians can use to help couples are presented. Mental health practitioners are encouraged to apply these principles to other specific irrationalities they may discover in their own work experience. (Author)
Block Toeplitz operators with rational symbols (II)
Hwang, In Sung [Department of Mathematics, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Lee, Woo Young [Department of Mathematics, Seoul National University, Seoul 151-742 (Korea, Republic of)], E-mail: ishwang@skku.edu, E-mail: wylee@math.snu.ac.kr
2008-09-26
In this paper we derive a formula for the rank of the self-commutator of hyponormal block Toeplitz operators T{sub {phi}} with matrix-valued rational symbols {phi} in L{sup {infinity}}(C{sup nxn}) via the classical Hermite-Fejer interpolation problem.
Block Toeplitz operators with rational symbols
Hwang, In Sung [Department of Mathematics, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Lee, Woo Young [Department of Mathematics, Seoul National University, Seoul 151-742 (Korea, Republic of)], E-mail: ishwang@skku.edu, E-mail: wylee@math.snu.ac.kr
2008-05-09
In this paper we show that the hyponormality of block Toeplitz operators T{sub {phi}} with matrix-valued rational symbols {phi} in L{sup {infinity}}(C{sup nxn}) is completely determined by the tangential Hermite-Fejer interpolation problem.
Summary Report on Rational Cryptographic Protocols
Alwen, Joël; Cachin, Christian; Pereira, Olivier
This report gives an overview of some of the models and techniques in rational cryptography, an emerging research area which in particular uses the methodologies and techniques of game theory to analyze cryptographic protocols and which uses cryptographic protocol theory to implement game theoretic...
Rational and Mechanistic Perspectives on Reinforcement Learning
Chater, Nick
2009-01-01
This special issue describes important recent developments in applying reinforcement learning models to capture neural and cognitive function. But reinforcement learning, as a theoretical framework, can apply at two very different levels of description: "mechanistic" and "rational." Reinforcement learning is often viewed in mechanistic terms--as…
Rationality and its limits in Arianism
Birjukov, Dmitry
2008-06-01
Full Text Available Having considered certain recurrent issues, such as the idea of comprehensibility of God and apopahtic theology, Dmitry Birjukov (Russian Christian Academy, St. Petersburg looks at the rational tendencies in Arianism and, on the basis of available data, shows how from Arius and Asterius to the Neo-Arians the rationalist tendencies in theology gradually increase while apophatic element virtually disappears.
Macroeconomics after Two Decades of Rational Expectations.
McCallum, Bennett T.
1994-01-01
Discusses real business cycle analysis, growth theory, and other economic concepts in the context of the rational expectations revolution in macroeconomics. Focuses on post-1982 research. Concludes that the rejuvenation of growth analysis is an encouraging development because it could lead to changes in welfare policy. (CFR)
A characterization of quasi-rational polygons
Bedaride, Nicolas
2012-11-01
The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced in Gutkin and Simányi (1992 Commun. Math. Phys. 143 431-49) and Schwartz (2009 Outer Billiards on Kites (Annals of Mathematics Studies vol 171) (Princeton, NJ: Princeton University Press)) and make a synthesis of them.
Rational Emotive Behavior Therapy: Humanism in Action.
Hill, Larry K.
1996-01-01
Claims that humanism, in both concept and philosophy, is encased in a literature that is predominantly abstract, making humanism difficult to translate into tangible day-to-day action. Argues that rational emotive behavior therapy (REBT), however, provides a detailed method for translating humanist concepts into humanist behavior. (RJM)
Critical Thinking and Rational Emotive Behavior Therapy.
Hatcher, Donald; Brown, Tony; Gariglietti, Kelli P.
2001-01-01
Notes limitations of Rational Emotive Behavior Therapy (REBT). Suggests that should these weaknesses be addressed, teachers of critical thinking would do well to incorporate REBT into their critical thinking courses. Relates that A. Ellis has suggested that the future of REBT is in integrating it into the educational curriculum as a way of…
Some Contemporary Rational Emotive Behavior Therapy Songs.
Watts, Richard E.
1996-01-01
Presents several new rational emotive behavior therapy (REBT) songs. Claims that the songs may be used in both academic and therapeutic settings as a humorous way to address cognitive distortions or irrational beliefs. Reports that students and clients have responded favorably to these songs. (RJM)
[Popper's critical rationalism and the biomedical sciences].
Havlícek, J
1993-11-08
Popper's rationalism makes an important contribution of the 20th century philosophy to the methodology of natural sciences. Through its criterion of falsification, it enabled the scientists to take a critical but constructive view on hypotheses, conjectures and theories. This attitude found its application also in medicine.
Viagra: : A success story for rationing?
Klein, R.; Sturm, H.
2002-01-01
The 1998 launch of Viagra prompted widespread fears about the budgetary consequences for insurers and governments, all the more so since Viagra was only the first of a new wave of so-called lifestyle drugs. The fears have turned out to be greatly exaggerated. This paper analyzes the rationing strate
Isomorphism, Homogeneity, and Rationalism in University Retrenchment.
Gates, Gordon S.
1997-01-01
Describes the process of retrenchment at a medium-sized state university (pseudonyms used) for the purpose of analyzing the isomorphic pressures (mimetic, coercive, normative) surfacing during the process and the role played by rationalism in decision-making. Draws on the literature of organizational theory and change, and makes comparisons with…
Disability and Rational Emotive Behavior Therapy (REBT).
Gandy, Gerald L.
This article provides information on how Rational Emotive Behavior Therapy (REBT) can be adapted for use in rehabilitation counseling. It states that although clients with an average range of intelligence have responded well to REBT, clients with borderline intellectual functioning are not suitable candidates for cognitive disputing but can be…
Critical Thinking and Rational Emotive Behavior Therapy.
Hatcher, Donald; Brown, Tony; Gariglietti, Kelli P.
2001-01-01
Notes limitations of Rational Emotive Behavior Therapy (REBT). Suggests that should these weaknesses be addressed, teachers of critical thinking would do well to incorporate REBT into their critical thinking courses. Relates that A. Ellis has suggested that the future of REBT is in integrating it into the educational curriculum as a way of…
Rational Emotive Behavior Therapy with Troubled Students.
Zionts, Paul; Zionts, Laura
1997-01-01
Based on the early work of Albert Ellis, seeks to identify and challenge irrational beliefs that underlie behavior problems. Outlines concepts and methods of Rational Emotive Behavior Theory and describes the application both in counseling and as a mental health curriculum for troubled children and youth. Offers classroom techniques. (RJM)