The rank of the semigroup of transformations stabilising a partition of a finite set
Araujo, Joao; Bentz, Wolfram; Mitchell, J. D.; Schneider, Csaba
2014-01-01
Let $\\mathcal{P}$ be a partition of a finite set $X$. We say that a full transformation $f:X\\to X$ preserves (or stabilizes) the partition $\\mathcal{P}$ if for all $P\\in \\mathcal{P}$ there exists $Q\\in \\mathcal{P}$ such that $Pf\\subseteq Q$. Let $T(X,\\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\\mathcal{P}$. In 2005 Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\\mathcal{P})$, when $\\mathcal{P}$ is a part...
The theory of finitely generated commutative semigroups
Rédei, L; Stark, M; Gravett, K A H
1966-01-01
The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before
Semigroups of transformations with fixed sets | Honyam ...
African Journals Online (AJOL)
Click on the link to view the abstract. Keywords: Transformation semigroup, Green's relations, ideal, rank. Quaestiones Mathematicae 36(2013), 79-92. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · http://dx.doi.org/10.2989/16073606.2013.779958 · AJOL African ...
Positive operator semigroups from finite to infinite dimensions
Bátkai, András; Rhandi, Abdelaziz
2017-01-01
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Permutation groups and transformation semigroups : results and problems
Araujo, Joao; Cameron, Peter Jephson
2015-01-01
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group $G$ and a single non-permutation $a$. Our particular concern is the influence that properties of $G$ (related to homogeneity, trans...
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
Nineteen papers on algebraic semigroups
Aizenshtat, A Ya; Podran, N E; Ponizovskii, IS; Shain, BM
1988-01-01
This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.
Hypercyclic Abelian Semigroups of Matrices on Cn
International Nuclear Information System (INIS)
Ayadi, Adlene; Marzougui, Habib
2010-07-01
We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)
Quotient semigroups and extension semigroups
Indian Academy of Sciences (India)
Introduction. Abelian groups and semigroups play an important role in the classification of C. ∗. -algebras and their extensions. ... -algebra extension theory and K K-theory, it is crucial to study the theory of quotient semigroups from the ...
Gaps in nonsymmetric numerical semigroups
International Nuclear Information System (INIS)
Fel, Leonid G.; Aicardi, Francesca
2006-12-01
There exist two different types of gaps in the nonsymmetric numerical semigroups S(d 1 , . . . , d m ) finitely generated by a minimal set of positive integers {d 1 , . . . , d m }. We give the generating functions for the corresponding sets of gaps. Detailed description of both gap types is given for the 1st nontrivial case m = 3. (author)
Neutrosophic Left Almost Semigroup
Directory of Open Access Journals (Sweden)
Mumtaz Ali
2014-06-01
Full Text Available In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties of neutrosophic LA-semigroup in this paper.
Remarks on numerical semigroups
International Nuclear Information System (INIS)
Torres, F.
1995-12-01
We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights state in [To]. (author). 25 refs
Numerical semigroups and applications
Assi, Abdallah
2016-01-01
This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher leve...
Quantitative recurrence for free semigroup actions
Carvalho, Maria; Rodrigues, Fagner B.; Varandas, Paulo
2018-03-01
We consider finitely generated free semigroup actions on a compact metric space and obtain quantitative information on Poincaré recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action. Besides, we relate the recurrence to balls with the rates of expansion of the semigroup generators and the topological entropy of the semigroup action. Finally, we establish a partial variational principle and prove an ergodic optimization for this kind of dynamical action. MC has been financially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER) under the partnership agreement PT2020. FR and PV were partially supported by BREUDS. PV has also benefited from a fellowship awarded by CNPq-Brazil and is grateful to the Faculty of Sciences of the University of Porto for the excellent research conditions.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
International Nuclear Information System (INIS)
El-Qallali, A.
1987-11-01
The least fundamental adequate good congruence on an arbitrary type W semigroup S is described as well as the largest superabundant full subsemigroup of S and the largest full subsemigroup of S which is a band of cancellative monoids. Weak type W semigroups are defined by replacing the idempotent-connected property in type W by one of its consequences and a structure theorem is obtained for such semigroups. (author). 12 refs
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
Entangling transformations in composite finite quantum systems
International Nuclear Information System (INIS)
Vourdas, A
2003-01-01
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,Z(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,Z(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically
On character amenability of semigroup algebras | Maepa ...
African Journals Online (AJOL)
We study the character amenability of semigroup algebras. We work on general semigroups and certain semigroups such as inverse semigroups with a nite number of idempotents, inverse semigroups with uniformly locally nite idempotent set, Brandt and Rees semigroup and study the character amenability of the ...
Finite field dependent mixed BRST transformation
International Nuclear Information System (INIS)
Upadhyay, Sudhaker; Mandal, Bhabani Prasad
2013-01-01
Joglekar and Mandal have generalized the usual Bechhi-Rouet-Stora-Tyutin (BRST) transformation by allowing infinitesimal BRST parameter finite and field dependent. Such a generalized BRST transformation (so-called FFBRST transformation) is also the symmetry of the effective action but not of the generating functional of the theory. We generalize the mixed BRST (sum of totally anti-commuting BRST and anti-BRST) symmetry transformation in same manner. We show that such a generalized mixed BRST transformation is the symmetry of the effective action as well as of the generating functional. We show our result by considering several explicit examples. (author)
Right $P$-comparable semigroups
Halimi, Nazer. H.
2009-01-01
In this paper we introduce the notion of right waist and right comparizer ideals for semigroups. In particular, we study the ideal theory of semigroups containing right waists and right comparizer ideals. We also study those properties of right cones that can be carried over to right $P$-comparable semigroups. We give sufficient and necessary conditions on the set of nilpotent elements of a semigroup to be an ideal. We provide several equivalent characterizations for a right ideal being a rig...
Directory of Open Access Journals (Sweden)
Seda OĞUZ ÜNAL
2016-10-01
Full Text Available Abstract. In this paper, necessary and sufficient conditions are studied for Bruck-Reilly and gener- alized Bruck-Reilly ∗-extensions of direct product of k monoids to be regular, unit regular, completely regular and orthodox. Moreover, we give an example of a finitely presented monoid (generalized Bruck-Reilly ∗-extension of Bruck-Reilly extension of a free group with infinite rank, the group of units of which is not finitely generated.2010 Mathematics Subject Classification: 16S15; 20E06; 20E22.Keywords and Phrases: Generalized Bruck-Reilly ∗-extension, finite generation, finite presentability. Özet. Bu makalede k tane monoidin direkt çarpımının Bruck-Reilly ve genelleştirilmiş Bruck-Reilly *- genişlemelerinin, regüler, terslenebilir regüler, tamamen regüler ve orthodox olabilmesi için gerek ve yeter koşullar çalışılmıştır. Ayrıca, biz terslenebilir elemanlarının grubu sonlu üreteçli olmayan sonlu sunumlu bir monoid (sonsuz ranklı bir serbest grubun Bruck-Reilly genişlemesinin genelleştirilmiş Bruck-Reilly *-genişlemesi örneği verdik. Anahtar Kelimeler: Genelleştirilmiş Bruck-Reilly *-genişlemesi, sonlu üreteçlilik, sonlu sunumluluk.
Decision problems for groups and semigroups
International Nuclear Information System (INIS)
Adian, S I; Durnev, V G
2000-01-01
The paper presents a detailed survey of results concerning the main decision problems of group theory and semigroup theory, including the word problem, the isomorphism problem, recognition problems, and other algorithmic questions related to them. The well-known theorems of Markov-Post, P.S. Novikov, Adian-Rabin, Higman, Magnus, and Lyndon are given with complete proofs. As a rule, the proofs presented in this survey are substantially simpler than those given in the original papers. For the sake of completeness, we first prove the insolubility of the halting problem for Turing machines, on which the insolubility of the word problem for semigroups is based. Specific attention is also paid to the simplest examples of semigroups with insoluble word problem. We give a detailed proof of the significant result of Lyndon that, in the class of groups presented by a system of defining relations for which the maximum mutual overlapping of any two relators is strictly less than one fifth of their lengths, the word problem is soluble, while insoluble word problems can occur when non-strict inequality is allowed. A proof of the corresponding result for finitely presented semigroups is also given, when the corresponding fraction is one half
Finite element simulation of piezoelectric transformers.
Tsuchiya, T; Kagawa, Y; Wakatsuki, N; Okamura, H
2001-07-01
Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.
Convergence semigroup categories
Directory of Open Access Journals (Sweden)
Gary Richardson
2013-09-01
Full Text Available Properties of the category consisting of all objects of the form (X, S, λ are investigated, where X is a convergence space, S is a commutative semigroup, and λ: X × S → X is a continuous action. A “generalized quotient” of each object is defined without making the usual assumption that for each fixed g ∈ S, λ(., g : X → X is an injection.
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de
2005-01-01
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail
Finite anticanonical transformations in field-antifield formalism
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A.; Tyutin, Igor V. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2015-06-15
We study the role of arbitrary (finite) anticanonical transformations in the field-antifield formalism and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered. (orig.)
Convergence semigroup actions: generalized quotients
Directory of Open Access Journals (Sweden)
H. Boustique
2009-10-01
Full Text Available Continuous actions of a convergence semigroup are investigated in the category of convergence spaces. Invariance properties of actions as well as properties of a generalized quotient space are presented
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
C-semigroup S(·) may not be densely defined and the perturbation operator B is a ... rems for local C-semigroups on X with densely defined generators. ...... [8] Shaw S-Y and Kuo C-C, Generation of local C-semigroups and solvability of the ...
The direct product of right zero semigroups and certain groupoids ...
African Journals Online (AJOL)
This paper investigates first the structure of semigroups which are direct products of right zero semigroups and cancellative semigroups with identity. We consider the relationship of these semigroups to right groups (the direct products of groups and right zero semigroups). Finally, we consider groupoids which are direct ...
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
A Novel Approach toward Fuzzy Generalized Bi-Ideals in Ordered Semigroups
Directory of Open Access Journals (Sweden)
Faiz Muhammad Khan
2014-01-01
Full Text Available In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples. These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups. Several fundamental theorems of ordered semigroups are investigated by the properties of these newly defined fuzzy generalized bi-ideals. Further, using level sets, ordinary fuzzy generalized bi-ideals are linked with these newly defined ideals which is the most significant part of this paper.
Theory of semigroups and applications
Sinha, Kalyan B
2017-01-01
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in...
Subharmonic projections for a quantum Markov semigroup
International Nuclear Information System (INIS)
Fagnola, Franco; Rebolledo, Rolando
2002-01-01
This article introduces a concept of subharmonic projections for a quantum Markov semigroup, in view of characterizing the support projection of a stationary state in terms of the semigroup generator. These results, together with those of our previous article [J. Math. Phys. 42, 1296 (2001)], lead to a method for proving the existence of faithful stationary states. This is often crucial in the analysis of ergodic properties of quantum Markov semigroups. The method is illustrated by applications to physical models
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
On Algebraic Study of Type-2 Fuzzy Finite State Automata
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Anupam K. Singh
2017-08-01
Full Text Available Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy transformation semigroup with a type-2 fuzzy finite state automata. Finally, we discuss several product of type-2 fuzzy finite state automata and shown that these product is a categorical product.
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S(⋅) may not be densely defined and the perturbation operator is a bounded linear operator from ¯D(A) into () such that = ...
On Embedding a Semigroup in a Group
Indian Academy of Sciences (India)
ias
the significance of semigroup theory. Commenting ... theory, I think it is not too strong to say, with scorn, because ... on G. The most natural example of a semigroup is the set M(A) of ..... group. Since cancellation laws hold in a group and hence.
Two-Valued States on Baer *-Semigroups
Freytes, Hector; Domenech, Graciela; de Ronde, Christian
2013-12-01
In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer *-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer *-semigroups.
Homology and cohomology of Rees semigroup algebras
DEFF Research Database (Denmark)
Grønbæk, Niels; Gourdeau, Frédéric; White, Michael C.
2011-01-01
Let S by a Rees semigroup, and let 1¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of l¹(S) is isomorphic to those of the underlying discrete group algebra....
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S ( ⋅ ) may not be densely defined and the perturbation operator is a bounded linear operator from D ( A ) ¯ into () such that = on D ( A ) ¯ ...
Stability of gradient semigroups under perturbations
Aragão-Costa, E. R.; Caraballo, T.; Carvalho, A. N.; Langa, J. A.
2011-07-01
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).
Stability of gradient semigroups under perturbations
International Nuclear Information System (INIS)
Aragão-Costa, E R; Carvalho, A N; Caraballo, T; Langa, J A
2011-01-01
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space)
Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Chill, Ralph; Tomilov, Yuri
2015-01-01
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern...
Construction of 2D quasi-periodic Rauzy tiling by similarity transformation
International Nuclear Information System (INIS)
Zhuravlev, V. G.; Maleev, A. V.
2009-01-01
A new approach to constructing self-similar fractal tilings is proposed based on the construction of semigroups generated by a finite set of similarity transformations. The Rauzy tiling-a 2D analog of 1D Fibonacci tiling generated by the golden mean-is used as an example to illustrate this approach. It is shown that the Rauzy torus development and the elementary fractal boundary of Rauzy tiling can be constructed in the form of a set of centers of similarity semigroups generated by two and three similarity transformations, respectively. A centrosymmetric tiling, locally dual to the Rauzy tiling, is constructed for the first time and its parameterization is developed.
Finite Countermodel Based Verification for Program Transformation (A Case Study
Directory of Open Access Journals (Sweden)
Alexei P. Lisitsa
2015-12-01
Full Text Available Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems.
Blockspin transformations for finite temperature field theories with gauge fields
International Nuclear Information System (INIS)
Kerres, U.
1996-08-01
A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)
Quantum dynamical semigroups and approach to equilibrium
International Nuclear Information System (INIS)
Frigerio, A.
1977-01-01
For a quantum dynamical semigroup possessing a faithful normal stationary state, some conditions are discussed, which ensure the uniqueness of the equilibrium state and/or the approach to equilibrium for arbitrary initial condition. (Auth.)
Inverse semigroups the theory of partial symmetries
Lawson, Mark V
1998-01-01
Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.
Quadratic forms for Feynman-Kac semigroups
International Nuclear Information System (INIS)
Hibey, Joseph L.; Charalambous, Charalambos D.
2006-01-01
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions
Weierstrass semigroups and the Feng-Rao Distance
DEFF Research Database (Denmark)
Campillo, Antonio; Farran, Ignacio
2000-01-01
We detrmine the Feng-Rao distance for several claases of codes from algebraic geometry usingthe weierstrass semigroups......We detrmine the Feng-Rao distance for several claases of codes from algebraic geometry usingthe weierstrass semigroups...
Construction of a Family of Quantum Ornstein-Uhlenbeck Semigroups
Ki Ko, C
2003-01-01
For a given quasi-free state on the CCR algebra over one dimensional Hilbert space, a family of Markovian semigroups which leave the quasi-free state invariant is constructed by means of noncommutative elliptic operators and Dirichlet forms on von Neumann algebras. The generators (Dirichlet operators) of the semigroups are analyzed and the spectrums together with eigenspaces are found. When restricted to a maximal abelian subalgebra, the semigroups are reduced to a unique Markovian semigroup of classical Ornstein-Uhlenbeck process.
Pei, Soo-Chang; Ding, Jian-Jiun
2005-03-01
Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Semigroups of Operators : Theory and Applications
Bobrowski, Adam; Lachowicz, Mirosław
2015-01-01
Many results, both from semigroup theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator the...
Semigroups of Herz-Schur multipliers
DEFF Research Database (Denmark)
Knudby, Søren
2014-01-01
function (see Theorem 1.2). It is then shown that a (not necessarily proper) generator of a semigroup of Herz–Schur multipliers splits into a positive definite kernel and a conditionally negative definite kernel. We also show that the generator has a particularly pleasant form if and only if the group...
On integral and finite Fourier transforms of continuous q-Hermite polynomials
International Nuclear Information System (INIS)
Atakishiyeva, M. K.; Atakishiyev, N. M.
2009-01-01
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
Application of finite Fourier transformation for the solution of the diffusion equation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1991-01-01
The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)
Relativistic elliptic matrix tops and finite Fourier transformations
Zotov, A.
2017-10-01
We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.
International Conference on Semigroups, Algebras and Operator Theory
Meakin, John; Rajan, A
2015-01-01
This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will f...
International Nuclear Information System (INIS)
Sen, S.; Balasubramaniam, R.; Sethuraman, R.
1996-01-01
The molar volume difference between the matrix and the precipitate phases in the case of solid state phase transformations results in the creation of stain energy in the system due to the misfit strains. A finite element model based on the initial strain approach is proposed to evaluate elasto-plastic accommodation energies during solid state transformation. The three-dimensional axisymmetric model has been used to evaluate energies as a function of transformation for α-β hydrogen transformations in the Nb-H system. The transformation has been analyzed for the cases of transformation progressing both from the center to surface and from the surface to center of the system. The effect of plastic deformation has been introduced to make the model realistic, specifically to the Nb-NbH phase transformation which involves a 4% linear misfit strain. It has been observed that plastic deformation reduces the strain energies compared to the linear elastic analysis
Maxwell superalgebras and Abelian semigroup expansion
Directory of Open Access Journals (Sweden)
P.K. Concha
2014-09-01
Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.
Maxwell superalgebras and Abelian semigroup expansion
Energy Technology Data Exchange (ETDEWEB)
Concha, P.K.; Rodríguez, E.K. [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Dipartimento di Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria, 1, 10125 Torino (Italy)
2014-09-15
The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM{sup (N)} recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sM{sub m+2} and their N-extended generalization can be obtained using the S-expansion procedure.
Semicrossed products of operator algebras by semigroups
Davidson, Kenneth R; Kakariadis, Evgenios T A
2017-01-01
The authors examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.
The Perron-Frobenius Theorem for Markov Semigroups
Hijab, Omar
2014-01-01
Let $P^V_t$, $t\\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius $e^{\\lambda_0t}$ of $P^V_t$, simultaneously for all $t\\ge0$. This is derived with no compactness assumption on the semigroup operators.
Efficient Finite Element Models for Calculation of the No-load losses of the Transformer
Directory of Open Access Journals (Sweden)
Kamran Dawood
2017-10-01
Full Text Available Different transformer models are examined for the calculation of the no-load losses using finite element analysis. Two-dimensional and three-dimensional finite element analyses are used for the simulation of the transformer. Results of the finite element method are also compared with the experimental results. The Result shows that 3-dimensional provide high accuracy as compared to the 2 dimensional full and half model. However, the 2-dimensional half model is the less time-consuming method as compared to the 3 and 2-dimensional full model. Simulation time duration taken by the different models of the transformer is also compared. The difference between the 3-dimensional finite element method and experimental results are less than 3%. These numerical methods can help transformer designers to minimize the development of the prototype transformers.
How to use the Fast Fourier Transform in Large Finite Fields
Petersen, Petur Birgir
2011-01-01
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
On the raising and lowering difference operators for eigenvectors of the finite Fourier transform
International Nuclear Information System (INIS)
Atakishiyeva, M K; Atakishiyev, N M
2015-01-01
We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)
Compactness of the difference between the porous thermoelastic semigroup and its decoupled semigroup
Directory of Open Access Journals (Sweden)
El Mustapha Ait Benhassi
2015-06-01
Full Text Available Under suitable assumptions, we prove the compactness of the difference between the porous thermoelastic semigroup and its decoupled one. This will be achieved by proving the norm continuity of this difference and the compactness of the difference between the resolvents of their generators. Applications to porous thermoelastic systems are given.
Classification of $E_{0}$-semigroups by product systems
Skeide, Michael
2016-01-01
In these notes the author presents a complete theory of classification of E_0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
Minimal prime ideals in semigroups without nilpotent elements
International Nuclear Information System (INIS)
Ahsan, J.
1989-07-01
The aim of this paper is to obtain a characterization of minimal prime ideals of (non-commutative) semigroups without nilpotent elements analogous to the one for the corresponding class of rings. We also define the notion of symmetric ideals of a semigroup and establish some of their basic properties. 5 refs
Semigroups of transcendental entire functions and their dynamics
Indian Academy of Sciences (India)
DINESH KUMAR
Abstract. We investigate the dynamics of semigroups of transcendental entire func- tions using Fatou–Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some condition for connectivity of the Julia set of the ...
On n-weak amenability of Rees semigroup algebras
Indian Academy of Sciences (India)
semigroups. In this work, we shall consider this class of Banach algebras. We examine the n-weak amenability of some semigroup algebras, and give an easier example of a Banach algebra which is n-weakly amenable if n is odd. Let L1(G) be the group algebra of a locally compact group G (§3.3 of [3]). Then Johnson.
Some aspects of non-linear semi-groups
International Nuclear Information System (INIS)
Plant, A.T.
1976-01-01
Some simpler theorems in the theory of non-linear semi-groups of non-reflexive Banach spaces are proved, with the intention to introduce the reader to this active field of research. Flow invariance, in particular for Lipschitz generators, and contraction semi-groups are discussed in some detail. (author)
Inverse operator of the generator of a C0-semigroup
Gomilko, A.M.; Zwart, Heiko J.; Tomilov, Y
2007-01-01
Let $A$ be the generator of a uniformly bounded $C_0$-semigroup in a Banach space $X$ such that $A$ has a trivial kernel and a dense range. The question whether $A^{-1}$ is a generator of a $C_0$-semigroup is considered. It is shown that the answer is negative in general for $X = \\ell_p$, $p \\in (1,
High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data
Morelli, Eugene A.
1997-01-01
Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.
Quantum number theoretic transforms on multipartite finite systems.
Vourdas, A; Zhang, S
2009-06-01
A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.
Semigroups, antiautomorphisms, and involutions: A computer solution to an open problem, I
International Nuclear Information System (INIS)
Winker, S.K.; Wos, L.; Lusk, E.L.
1981-01-01
An antiautomorphism H of a semigroup S is a 1-1 mapping of S onto itself such that H(xy) = H(y)H(x) for all x,y in S. An antiautomorphism H is an involution if H 2 (x) = x for all x in S. In this paper the following question is answered: Does there exist a finite semigroup with antiautomorphism but no involution. This question, suggested by I. Kaplansky, was answered in the affirmative with the aid of an automated theorem-proving program. More precisely, there are exactly four such semigroups of order seven and none of smaller order. The program was a completely general one, and did not calculate the solution directly, but rather rendered invaluable assistance to the mathematicians investigating the question by helping to generate and examine various models. A detailed discussion of the approach is presented, with the intention of demonstrating the usefulness of a theorem prover in carrying out certain types of mathematical research
On the finite Fourier transforms of functions with infinite discontinuities
Directory of Open Access Journals (Sweden)
Branko Saric
2002-01-01
Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.
An application of $\\Gamma$-semigroups techniques to the Green's Theorem
Kehayopulu, Niovi
2017-01-01
The concept of a $\\Gamma$-semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green's relations play an essential role in studying the structure of semigroups. In the present paper we deal with an application of $\\Gamma$-semigroups techniques to the Green's Theorem in an attempt to show the way we pass from semigroups to $\\Gamma$-semigroups.
Directory of Open Access Journals (Sweden)
Lei Wang
2015-09-01
Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.
International Nuclear Information System (INIS)
Takeshi, Y.; Keisuke, K.
1983-01-01
The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method
Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
Eberle, Andreas
1999-01-01
This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.
3-D spherical harmonics code FFT3 by the finite Fourier transformation method
International Nuclear Information System (INIS)
Kobayashi, K.
1997-01-01
In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)
Fixed point theorems for generalized Lipschitzian semigroups
Directory of Open Access Journals (Sweden)
Jong Soo Jung
2001-01-01
semigroup of K into itself, that is, for s∈G, ‖Tsx−Tsy‖≤as‖x−y‖+bs(‖x−Tsx‖+‖y−Tsy‖+cs(‖x−Tsy‖+‖y−Tsx‖, for x,y∈K where as,bs,cs>0 such that there exists a t1∈G such that bs+cs<1 for all s≽t1. It is proved that if there exists a closed subset C of K such that ⋂sco¯{Ttx:t≽s}⊂C for all x∈K, then with [(α+βp(αp⋅2p−1−1/(cp−2p−1βp⋅Np]1/p<1 has a common fixed point, where α=lim sups(as+bs+cs/(1-bs-cs and β=lim sups(2bs+2cs/(1-bs-cs.
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Sergyeyev, Artur [Mathematical Institute, Silesian University in Opava, Na RybnIcku 1, 746 01 Opava (Czech Republic); Blaszak, Maciej [Institute of Physics, A Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland)], E-mail: Artur.Sergyeyev@math.slu.cz, E-mail: blaszakm@amu.edu.pl
2008-03-14
We present a multiparameter generalization of the Staeckel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized Staeckel transform preserves Liouville integrability, noncommutative integrability and superintegrability. The corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form, and we investigate the properties of this reciprocal transformation. Finally, we show that the Hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized Staeckel transform.
Lei Wang; Hongjun Yin; Xiaoshuang Yang; Chuncheng Yang; Jing Fu
2015-01-01
Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare wi...
Tensor products and regularity properties of Cuntz semigroups
Antoine, Ramon; Thiel, Hannes
2018-01-01
The Cuntz semigroup of a C^*-algebra is an important invariant in the structure and classification theory of C^*-algebras. It captures more information than K-theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C^*-algebra A, its (concrete) Cuntz semigroup \\mathrm{Cu}(A) is an object in the category \\mathrm{Cu} of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter \\mathrm{Cu}-semigroups. The authors establish the existence of tensor products in the category \\mathrm{Cu} and study the basic properties of this construction. They show that \\mathrm{Cu} is a symmetric, monoidal category and relate \\mathrm{Cu}(A\\otimes B) with \\mathrm{Cu}(A)\\otimes_{\\mathrm{Cu}}\\mathrm{Cu}(B) for certain classes of C^*-algebras. As a main tool for their approach the authors introduce the category \\mathrm{W} of ...
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
1977-01-01
An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
Fourier transform and the Verlinde formula for the quantum double of a finite group
Koornwinder, T.H.; Schroers, B.J.; Slingerland, J.K.; Bais, F.A.
1999-01-01
We define a Fourier transform $S$ for the quantum double $D(G)$ of a finite group $G$. Acting on characters of $D(G)$, $S$ and the central ribbon element of $D(G)$ generate a unitary matrix representation of the group $SL(2,Z)$. The characters form a ring over the integers under both the algebra
Symmetries of the second-difference matrix and the finite Fourier transform
International Nuclear Information System (INIS)
Aguilar, A.; Wolf, K.B.
1979-01-01
The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)
Fedorenko, Sergei V.
2011-01-01
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.
Platt, P.; Frankel, P.; Gass, M.; Howells, R.; Preuss, M.
2014-11-01
Corrosion is a key limiting factor in the degradation of zirconium alloys in light water reactors. Developing a mechanistic understanding of the corrosion process offers a route towards improving safety and efficiency as demand increases for higher burn-up of fuel. Oxides formed on zirconium alloys are composed of both monoclinic and meta-stable tetragonal phases, and are subject to a number of potential mechanical degradation mechanisms. The work presented investigates the link between the tetragonal to monoclinic oxide phase transformation and degradation of the protective character of the oxide layer. To achieve this, Abaqus finite element analysis of the oxide phase transformation has been carried out. Study of the change in transformation strain energy shows how relaxation of oxidation induced stress and fast fracture at the metal-oxide interface could destabilise the tetragonal phase. Central to this is the identification of the transformation variant most likely to form, and understanding why twinning of the transformed grain is likely to occur. Development of transformation strain tensors and analysis of the strain components allows some separation of dilatation and shear effects. Maximum principal stress is used as an indication of fracture in the surrounding oxide layer. Study of the stress distributions shows the way oxide fracture is likely to occur and the differing effects of dilatation and shape change. Comparison with literature provides qualitative validation of the finite element simulations.
International Nuclear Information System (INIS)
Platt, P.; Frankel, P.; Gass, M.; Howells, R.; Preuss, M.
2014-01-01
Corrosion is a key limiting factor in the degradation of zirconium alloys in light water reactors. Developing a mechanistic understanding of the corrosion process offers a route towards improving safety and efficiency as demand increases for higher burn-up of fuel. Oxides formed on zirconium alloys are composed of both monoclinic and meta-stable tetragonal phases, and are subject to a number of potential mechanical degradation mechanisms. The work presented investigates the link between the tetragonal to monoclinic oxide phase transformation and degradation of the protective character of the oxide layer. To achieve this, Abaqus finite element analysis of the oxide phase transformation has been carried out. Study of the change in transformation strain energy shows how relaxation of oxidation induced stress and fast fracture at the metal–oxide interface could destabilise the tetragonal phase. Central to this is the identification of the transformation variant most likely to form, and understanding why twinning of the transformed grain is likely to occur. Development of transformation strain tensors and analysis of the strain components allows some separation of dilatation and shear effects. Maximum principal stress is used as an indication of fracture in the surrounding oxide layer. Study of the stress distributions shows the way oxide fracture is likely to occur and the differing effects of dilatation and shape change. Comparison with literature provides qualitative validation of the finite element simulations
Energy Technology Data Exchange (ETDEWEB)
Platt, P., E-mail: Philip.Platt@manchester.ac.uk [University of Manchester, School of Materials, Materials Performance Centre, Manchester M13 9PL (United Kingdom); Frankel, P. [University of Manchester, School of Materials, Materials Performance Centre, Manchester M13 9PL (United Kingdom); Gass, M.; Howells, R. [AMEC, Walton House, Faraday Street, Birchwood Park, Risley, Warrington WA3 6GA (United Kingdom); Preuss, M. [University of Manchester, School of Materials, Materials Performance Centre, Manchester M13 9PL (United Kingdom)
2014-11-15
Corrosion is a key limiting factor in the degradation of zirconium alloys in light water reactors. Developing a mechanistic understanding of the corrosion process offers a route towards improving safety and efficiency as demand increases for higher burn-up of fuel. Oxides formed on zirconium alloys are composed of both monoclinic and meta-stable tetragonal phases, and are subject to a number of potential mechanical degradation mechanisms. The work presented investigates the link between the tetragonal to monoclinic oxide phase transformation and degradation of the protective character of the oxide layer. To achieve this, Abaqus finite element analysis of the oxide phase transformation has been carried out. Study of the change in transformation strain energy shows how relaxation of oxidation induced stress and fast fracture at the metal–oxide interface could destabilise the tetragonal phase. Central to this is the identification of the transformation variant most likely to form, and understanding why twinning of the transformed grain is likely to occur. Development of transformation strain tensors and analysis of the strain components allows some separation of dilatation and shear effects. Maximum principal stress is used as an indication of fracture in the surrounding oxide layer. Study of the stress distributions shows the way oxide fracture is likely to occur and the differing effects of dilatation and shape change. Comparison with literature provides qualitative validation of the finite element simulations.
Finite size effects in phase transformation kinetics in thin films and surface layers
International Nuclear Information System (INIS)
Trofimov, Vladimir I.; Trofimov, Ilya V.; Kim, Jong-Il
2004-01-01
In studies of phase transformation kinetics in thin films, e.g. crystallization of amorphous films, until recent time is widely used familiar Kolmogorov-Johnson-Mehl-Avrami (KJMA) statistical model of crystallization despite it is applicable only to an infinite medium. In this paper a model of transformation kinetics in thin films based on a concept of the survival probability for randomly chosen point during transformation process is presented. Two model versions: volume induced transformation (VIT) when the second-phase grains nucleate over a whole film volume and surface induced transformation (SIT) when they form on an interface with two nucleation mode: instantaneous nucleation at transformation onset and continuous one during all the process are studied. At VIT-process due to the finite film thickness effects the transformation profile has a maximum in a film middle, whereas that of the grains population reaches a minimum inhere, the grains density is always higher than in a volume material, and the thinner film the slower it transforms. The transformation kinetics in a thin film obeys a generalized KJMA equation with parameters depending on a film thickness and in limiting cases of extremely thin and thick film it reduces to classical KJMA equation for 2D- and 3D-system, respectively
Semi-groups of operators and some of their applications to partial differential equations
International Nuclear Information System (INIS)
Kisynski, J.
1976-01-01
Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)
International Nuclear Information System (INIS)
Prakash, A; Lebensohn, R A
2009-01-01
In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
The fractional finite Hankel transform and its applications in fractal space
International Nuclear Information System (INIS)
Jiang Xiaoyun; Xu Mingyu
2009-01-01
In the present work, a generalized finite Hankel transform is derived which is useful in solving equations in fractal dimension d f and involving a fractal diffusion coefficient D 0 r -θ . The corresponding inversion formula is established and some properties are given. Then, the transform is successfully used to solve a class of time-fractional diffusion equations in fractional spatial dimension with an absorbent term and Schroedinger equation in fractional-dimensional space. Green's functions and exact wave function of the above problems are found.
Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.
Lange, K
1982-03-01
In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.
International Nuclear Information System (INIS)
Mori, N.; Kobayashi, K.
1996-01-01
A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)
Semigroups of analytic functions in analysis and applications
International Nuclear Information System (INIS)
Goryainov, Victor V
2012-01-01
This survey considers problems of analysis and certain related areas in which semigroups of analytic functions with respect to the operation of composition appear naturally. The main attention is devoted to holomorphic maps of a disk (or a half-plane) into itself. The role of fixed points is highlighted, both in the description of the structure of semigroups and in applications. Interconnections of the problem of fractional iteration with certain problems in the theory of random branching processes are pointed out, as well as with certain questions of non-commutative probability. The role of the infinitesimal description of semigroups of conformal maps in the development of the parametric method in the theory of univalent functions is shown. Bibliography: 94 titles.
On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2008-01-01
It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity
Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.
2009-01-01
It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
Vibration Finite Element Analysis of SC10 Dry-type Transformer Core
Directory of Open Access Journals (Sweden)
Gao Sheng Wei
2014-06-01
Full Text Available As the popularization and application of dry-type power transformer, its work when the vibration noise problem widely concerned, on the basis of time-varying electromagnetic field and structural mechanics equation, this paper established a finite element analysis model of dry-type transformer, through the electromagnetic field – Structural mechanics field – sound field more than physical field coupling calculation analysis, obtained in no load and the vibration modes of the core under different load and frequency. According to the transformer vibration mechanism, compared with the experimental data, verified the accuracy of the calculation results, as the core of how to provide the theory foundation and to reduce the noise of the experiment.
Energy Technology Data Exchange (ETDEWEB)
Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic)
2012-06-04
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
International Nuclear Information System (INIS)
Sergyeyev, Artur
2012-01-01
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
Spectral analysis of linear relations and degenerate operator semigroups
International Nuclear Information System (INIS)
Baskakov, A G; Chernyshov, K I
2002-01-01
Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1977-01-01
A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)
International Nuclear Information System (INIS)
Stupkiewicz, S.; Petryk, H.
2006-01-01
A micromechanical model of stress-induced martensitic transformation in single crystals of shape memory alloys is developed. This model is a finite-strain counterpart to the approach presented recently in the small-strain setting [S. Stupkiewicz, H. Petryk, J. Mech. Phys. Solids 50 (2002) 2303-2331]. The stress-induced transformation is assumed to proceed by the formation and growth of parallel martensite plates within the austenite matrix. Propagation of phase transformation fronts is governed by a rate-independent thermodynamic criterion with a threshold value for the thermodynamic driving force, including in this way the intrinsic dissipation due to phase transition. This criterion selects the initial microstructure at the onset of transformation and governs the evolution of the laminated microstructure at the macroscopic level. A multiplicative decomposition of the deformation gradient into elastic and transformation parts is assumed, with full account for the elastic anisotropy of the phases. The pseudoelastic behavior of Cu-Zn-Al single crystal in tension and compression is studied as an application of the model
Performance analysis of a finite radon transform in OFDM system under different channel models
Energy Technology Data Exchange (ETDEWEB)
Dawood, Sameer A.; Anuar, M. S.; Fayadh, Rashid A. [School of Computer and Communication Engineering, Universiti Malaysia Perlis (UniMAP) Pauh Putra, 02000 Arau, Parlis (Malaysia); Malek, F.; Abdullah, Farrah Salwani [School of Electrical System Engineering, Universiti Malaysia Perlis (UniMAP) Pauh Putra, 02000 Arau, Parlis (Malaysia)
2015-05-15
In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.
Performance analysis of a finite radon transform in OFDM system under different channel models
International Nuclear Information System (INIS)
Dawood, Sameer A.; Anuar, M. S.; Fayadh, Rashid A.; Malek, F.; Abdullah, Farrah Salwani
2015-01-01
In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Bering, Klaus [Masaryk University, Faculty of Science, Brno (Czech Republic); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2016-03-15
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived. (orig.)
Conference on Arithmetic and Ideal Theory of Rings and Semigroups
Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce
2016-01-01
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
SEMIGROUPS N TIMES INTEGRATED AND AN APPLICATION TO A PROBLEM OF CAUCHY TYPE
Directory of Open Access Journals (Sweden)
Danessa Chirinos Fernández
2016-06-01
Full Text Available The theory of semigroups n times integrated is a generalization of strongly continuous semigroups, which was developed from 1984, and is widely used for the study of the existence and uniqueness of problems such Cauchy in which the operator domain is not necessarily dense. This paper presents an application of semigroups n times integrated into a problem of viscoelasticity, which is formulated as a Cauchy problem on a Banach space presents .
An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars; Kaplan, Haim
2012-01-01
Let S be a set of n intervals in $\\mathbb{R}$, and let $(\\mathbf{S}, +)$ be any commutative semigroup. We assign a weight $\\omega(s) \\in \\mathbf{S}$ to each interval in S. For a point $x \\in \\mathbb{R}$, let $S(x) \\subseteq S$ be the set of intervals that contain x. Given a point $q \\in \\mathbb{R...
Dimension counts for singular rational curves via semigroups
Cotterill, Ethan; Feital, Lia; Martins, Renato Vidal
2015-01-01
We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\\mb{P}^n$, holds whenever $g$ is small.
Soft Neutrosophic Bi-LA-semigroup and Soft Neutrosophic N-LA-seigroup
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Mumtaz Ali
2014-09-01
Full Text Available Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic biLA-semigroup,soft neutosophic sub bi-LA-semigroup, soft neutrosophic N -LA-semigroup with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic bi-LAsemigroup, the so called soft strong neutrosophic bi-LAsemigoup which is of pure neutrosophic character. This is also extend to soft neutrosophic strong N-LA-semigroup. We also given some of their properties of this newly born soft structure related to the strong part of neutrosophic theory.
International Nuclear Information System (INIS)
Liu, B; Raabe, D; Roters, F; Eisenlohr, P; Lebensohn, R A
2010-01-01
We compare two full-field formulations, i.e. a crystal plasticity fast Fourier transform-based (CPFFT) model and the crystal plasticity finite element model (CPFEM) in terms of the deformation textures predicted by both approaches. Plane-strain compression of a 1024-grain ensemble is simulated with CPFFT and CPFEM to assess the models in terms of their predictions of texture evolution for engineering applications. Different combinations of final textures and strain distributions are obtained with the CPFFT and CPFEM models for this 1024-grain polycrystal. To further understand these different predictions, the correlation between grain rotations and strain gradients is investigated through the simulation of plane-strain compression of bicrystals. Finally, a study of the influence of the initial crystal orientation and the crystallographic neighborhood on grain rotations and grain subdivisions is carried out by means of plane-strain compression simulations of a 64-grain cluster
Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.
Liang, Zhichun; Crepeau, Richard H; Freed, Jack H
2005-12-01
Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
A noncommutative mean ergodic theorem for partial W*-dynamical semigroups
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1992-12-01
A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
Nearrings some developments linked to semigroups and groups
Ferrero, Celestina Cotti
2002-01-01
This work presents new and old constructions of nearrings. Links between properties of the multiplicative of nearrings (as regularity conditions and identities) and the structure of nearrings are studied. Primality and minimality properties of ideals are collected. Some types of `simpler' nearrings are examined. Some nearrings of maps on a group are reviewed and linked with group-theoretical and geometrical questions. Audience: Researchers working in nearring theory, group theory, semigroup theory, designs, and translation planes. Some of the material will be accessible to graduate students.
Refinement monoids, equidecomposability types, and boolean inverse semigroups
Wehrung, Friedrich
2017-01-01
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Analytic semigroups and optimal regularity in parabolic problems
Lunardi, Alessandra
2012-01-01
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p
On a finite moment perturbation of linear functionals and the inverse Szegö transformation
Directory of Open Access Journals (Sweden)
Edinson Fuentes
2016-05-01
Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.
Directory of Open Access Journals (Sweden)
M. Jamali
2011-09-01
Full Text Available The phenomenon of magnetizing inrush is a transient condition, which occurs primarily when a transformer is energized. The magnitude of inrush current may be as high as ten times or more times of transformer rated current that causes malfunction of protection system. So, for safe running of a transformer, it is necessary to distinguish inrush current from fault currents. In this paper, an equivalent instantaneous inductance (EII technique is used to discriminate inrush current from fault currents. For this purpose, a three-phase power transformer has been simulated in Maxwell software that is based on finite elements. This three-phase power transformer has been used to simulate different conditions. Then, the results have been used as inputs in MATLAB program to implement the equivalent instantaneous inductance technique. The results show that in the case of inrush current, the equivalent instantaneous inductance has a drastic variation, while it is almost constant in the cases of fault conditions.
International Conference on Lattices, Semigroups, and Universal Algebra
Bordalo, Gabriela; Dwinger, Philip
1990-01-01
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories ha...
International Nuclear Information System (INIS)
Kraus, H.G.
1991-01-01
This paper discusses methods for calculating Fraunhofer intensity fields resulting from diffraction through one- and two-dimensional apertures are presented. These methods are based on the geometric concept of finite elements and on Fourier and Abbe transforms. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define aperture(s) of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s) which may be of continuous or discontinuous form. The transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is most evident in two dimensions, where several examples are presented which include secondary obstructions, straight and curved secondary spider supports, multiple-mirror arrays, synthetic aperture arrays, segmented mirrors, apertures covered by screens, apodization, and phase plates. Typically, the finite element Abbe transform method results in significant gains in computational efficiency over the finite element Fourier transform method, but is also subject to some loss in generality
Basak, Anup; Levitas, Valery I.
2018-04-01
A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.
C0-semigroups of linear operators on some ultrametric Banach spaces
Directory of Open Access Journals (Sweden)
Toka Diagana
2006-01-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
International Nuclear Information System (INIS)
Yazdani-Asrami, Mohammad; Mirzaie, Mohammad; Shayegani Akmal, Amir Abbas
2013-01-01
Transformers are basically designed to operate under nominal voltage, rated frequency and also, pure sinusoidal load current. In recent decade, change in the type of loads and increasing use of power electronic devices with their nonsinusoidal current waveform has distorted the system voltage waveform as well. The losses of transformers include load and no-load losses. No-load loss continuously led to loss of energy in transformers that are connected to the network in all 24 h. With respect to high significance of energy and undesirable impacts of losses on the aging of transformers, the no-load loss is considered as a critical factor. Nowadays, it is necessary to apply a suitable method for calculation of no-load loss in presence of the voltage harmonics and over-excite conditions, especially for distribution transformers, as a result of harmonic increase in the voltage and current in the network and particular applications. In this paper, Finite Element Method (FEM) has been used to simulate nonsinusoidal voltage effects on no-load loss of transformers. Such simulation enables the software to simulate and analyze different electromagnetic parameters such as flux lines, flux density, losses, and etc under different input sources and with high accuracy. In addition, effect of nonsinusoidal voltages on no-load loss has been investigated by a typical experimental transformer using several practical tests. - Highlights: ► FEM has been employed to loss calculation of distribution transformer under distorted voltages. ► This method gives accurate results in comparison with standard or circuit based methods. ► A new version of 3D FEM has been used, this approach is electromagnetic based. ► In literature, FEM always used for study of transformer load loss and most of them based on magneto-static FEM. ► FEM results are validated by experiment for small test transformer
International Nuclear Information System (INIS)
Zhao Yunbin
2010-01-01
While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.
Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay
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Hassane Bouzahir
2007-02-01
Full Text Available We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.
On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup
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S.A. Grigoryan
2016-06-01
Full Text Available The class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be Z-graded С*-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed.
Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)
International Nuclear Information System (INIS)
Kumar, V.; Sahni, D.C.
1983-01-01
In this paper, the authors present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a homogeneous cylinder of finite height with general anisotropic scattering. They present the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the S/sub N/ method of TWOTRAN
Positivity and monotonicity properties of C0-semigroups. Pt. 1
International Nuclear Information System (INIS)
Bratteli, O.; Kishimoto, A.; Robinson, D.W.
1980-01-01
If exp(-tH), exp(-tK), are self-adjoint, positivity preserving, contraction semigroups on a Hilbert space H = L 2 (X;dμ) we write esup(-tH) >= esup(-tK) >= 0 whenever exp(-tH) - exp(-tK) is positivity preserving for all t >= 0 and then we characterize the class of positive functions for which (*) always implies esup(-tf(H)) >= esup(-tf(K)) >= 0. This class consists of the f epsilon Csup(infinitely)(0, infinitely) with (-1)sup(n)fsup((n + 1))(x) >= 0, x epsilon(0, infinitely), n = 0, 1, 2, ... In particular it contains the class of monotone operator functions. Furthermore if exp(-tH) is Lsup(P)(X;dμ) contractive for all p epsilon[1, infinitely] and all t > 0 (or, equivalently, for p = infinitely and t > 0) then exp(-tf(H)) has the same property. Various applications to monotonicity properties of Green's functions are given. (orig.)
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C
1993-10-01
Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)
Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping
2017-07-01
This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.
International Nuclear Information System (INIS)
Datta, K.; Geijselaers, H. J. M.; Huetink, J.; Post, J.; Dinsdale, A.
2007-01-01
The mechanics and thermodynamics of strain induced martensitic transformation are coupled for a metastable alloy steel and implemented in FE models of forming processes. The basic formulations are based on a fifty year old treaty by Patel and Cohen. The variation in Gibbs energy due to local variation in strain, strain rate, temperature and state of stress of a forming part is calculated by FE codes. The local variation in Gibbs energy gives a probabilistic image of the potential sites for strain induced martensitic transformations
International Nuclear Information System (INIS)
Ganapol, B.D.; Sumini, M.
1990-01-01
The time dependent space second order discrete form of the monokinetic transport equation is given an analytical solution, within the Laplace transform domain. Th A n dynamic model is presented and the general resolution procedure is worked out. The solution in the time domain is then obtained through the application of a numerical transform inversion technique. The justification of the research relies in the need to produce reliable and physically meaningful transport benchmarks for dynamic calculations. The paper is concluded by a few results followed by some physical comments
Conformational transformations induced by the charge-curvature interaction at finite temperature
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Gorria, Carlos; Christiansen, Peter Leth
2008-01-01
The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both...
International Nuclear Information System (INIS)
Das, R.N.
1980-01-01
The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)
A semigroup approach to the strong ergodic theorem of the multistate stable population process.
Inaba, H
1988-01-01
"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt
Functional calculus for C0-semigroups using infinite-dimensional systems theory
Schwenninger, F.L.; Zwart, Hans; Arendt, Wolfgang; Chill, Ralph; Tomilov, Yuri
2015-01-01
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in functional calculus.
Renardy, M.
1981-10-01
A semigroup approach to differential-delay equations is developed which seems more suitable for certain partial integro-differential equations than the standard theory. On a formal level, it is demonstrated that the stretching of filaments of viscoelastic liquids can be described by an equation of this form.
A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions
Directory of Open Access Journals (Sweden)
Kamonrat Nammanee
2012-01-01
Full Text Available We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞. Our results improve and extend those announced by G. Marino and H.-K. Xu (2006 and many authors.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
International Nuclear Information System (INIS)
Kobayashi, K.
1995-01-01
A simple formulation to derive second order differential equations of the spherical harmonics method is described, and it is shown that there is difficulty in deriving finite difference equations for these differential equations at material interfaces, because the second order differential terms of higher order moments must be expressed by the values in a mesh box. On the other hand, it is shown that there is no such difficulty, if the author uses the finite Fourier transformation method, since the differential equations are transformed into integral equations and the differentiation corresponds simply to a multiplication by the transformation parameter. Solution can be obtained in the form of Fourier series without making use of the inversion integral
Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space
Lemle, Ludovic Dan; Wu, Liming
2007-01-01
The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\\R^d,dx)$ weak solution.
Representation theory of finite monoids
Steinberg, Benjamin
2016-01-01
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional ...
Talaghat, Mohammad Reza; Jokar, Seyyed Mohammad
2017-12-01
This article offers a study on estimation of heat transfer parameters (coefficient and thermal diffusivity) using analytical solutions and experimental data for regular geometric shapes (such as infinite slab, infinite cylinder, and sphere). Analytical solutions have a broad use in experimentally determining these parameters. Here, the method of Finite Integral Transform (FIT) was used for solutions of governing differential equations. The temperature change at centerline location of regular shapes was recorded to determine both the thermal diffusivity and heat transfer coefficient. Aluminum and brass were used for testing. Experiments were performed for different conditions such as in a highly agitated water medium ( T = 52 °C) and in air medium ( T = 25 °C). Then, with the known slope of the temperature ratio vs. time curve and thickness of slab or radius of the cylindrical or spherical materials, thermal diffusivity value and heat transfer coefficient may be determined. According to the method presented in this study, the estimated of thermal diffusivity of aluminum and brass is 8.395 × 10-5 and 3.42 × 10-5 for a slab, 8.367 × 10-5 and 3.41 × 10-5 for a cylindrical rod and 8.385 × 10-5 and 3.40 × 10-5 m2/s for a spherical shape, respectively. The results showed there is close agreement between the values estimated here and those already published in the literature. The TAAD% is 0.42 and 0.39 for thermal diffusivity of aluminum and brass, respectively.
Polynômes orthogonaux avec argument matriciel et les semigroupes associés
Balderrama , Cristina
2009-01-01
In this work we construct and study families of generalized orthogonal polynomials with hermitian matrix argument associated to a family of orthogonal polynomials on R. Different normalizations for these polynomials are considered and we obtain some classical formulas for orthogonal polynomials from the corresponding formulas for the one–dimensional polynomials. We also construct semigroups of operators associated to the generalized orthogonal polynomials and we give an expression of the infi...
Some problems on non-linear semigroups and the blow-up of integral solutions
International Nuclear Information System (INIS)
Pavel, N.H.
1983-07-01
After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions
Analysis of the dynamic behavior of an intense charged particle beam using the semigroup approach
International Nuclear Information System (INIS)
Stafford, M.A.
1984-01-01
Dynamic models of a charged particle beam subject to external electromagnetic fields are cast into the abstract Cauchy problem form. Various applications of intense charged particle beams, i.e., beams whose self electromagnetic fields are significant, might require, or be enhanced by, the use of dynamic control constructed from suitably processed measurements of the state of the beam. This research provides a mathematical foundation for future engineering development of estimation and control designs for such beams. Beginning with the Vlasov equation, successively simpler models of intense beams are presented, along with their corresponding assumptions. Expression of a model in abstract Cauchy problem form is useful in determining whether the model is well posed. Solutions of well-posed problems can be expressed in terms of a one-parameter semigroup of linear operators. The semigroup point of view allows the application of the rapidly maturing modern control theory of infinite dimensional system. An appropriate underlying Banach space is identified for a simple, but nontrivial, single degree of freedom model (the electrostatic approximation model), and the associated one-parameter semigroup of linear operators is characterized
Zhao, Xue-Hui; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Sun, Yan; Guo, Yong-Jiang
2018-04-01
Under investigation in this paper is a (2+1)-dimensional Davey-Stewartson system, which describes the transformation of a wave-packet on water of finite depth. By virtue of the bell polynomials, bilinear form, Bäcklund transformation and Lax pair are got. One- and two-soliton solutions are obtained via the symbolic computation and Hirota method. Velocity and amplitude of the one-soliton solutions are relevant with the wave number. Graphical analysis indicates that soliton shapes keep unchanged and maintain their original directions and amplitudes during the propagation. Elastic overtaking and head-on interactions between the two solitons are described.
Subramaniam, B; Claudius, J S
1990-03-08
Cancer therapy using chemotherapeutic drugs frequently involves injection of the drug into the body through some intravenous mode of administration, viz, continuous (drip) infusion or single/multiple bolus injection(s). An understanding of the effect of the various modes of administration upon tumor penetration of drug is essential to rational design of drug therapy. This paper investigates drug penetration into a model tumor of slab geometry (between two capillaries) in which the overall transport rate of drug is limited by intra-tumor transport characterized by an effective diffusion coefficient. Employing the method of Finite Fourier Transforms (FFT), analytical solutions have been obtained for transient drug distribution in both the plasma and the tumor following three modes of administration, viz, continuous infusion, single bolus injection and equally-spaced equal-dose multiple bolus injections, of a given amount of drug. The qualitative trends exhibited by the plasma drug distribution profiles are consistent with reported experimental studies. Two concepts, viz, the dimensionless decay constant and the plasma/tumor drug concentration trajectories, are found to be particularly useful in the rational design of drug therapy. The dimensionless decay constant provides a measure of the rate of drug decay in the plasma relative to the rate of drug diffusion into the tumor and is thus characteristic of the tumor/drug system. The magnitude of this parameter dictates the choice of drug administration mode for minimizing drug decay in the plasma while simultaneously maximizing drug transport into the tumor. The concentration trajectories provide a measure of the plasma drug concentration relative to the tumor drug concentration at various times following injection. When the tumor drug concentration exceeds the plasma drug concentration, the drug will begin to diffuse out of the tumor. Knowledge of the time at which this diffusion reversal occurs is especially useful
Tica, Christian D.; Galapon, Eric A.
2018-02-01
The paper addresses the exact evaluation of the generalized Stieltjes transform Sn[f ] =∫0∞f (x ) (ω+x ) -nd x of integral order n = 1, 2, 3, … about ω = 0 from which the asymptotic behavior of Sn[f] for small parameters ω is directly extracted. An attempt to evaluate the integral by expanding the integrand (ω + x)-n about ω = 0 and then naively integrating the resulting infinite series term by term leads to an infinite series whose terms are divergent integrals. Assigning values to the divergent integrals, say, by analytic continuation or by Hadamard's finite part is known to reproduce only some of the correct terms of the expansion but completely misses out a group of terms. Here we evaluate explicitly the generalized Stieltjes transform by means of finite-part integration recently introduced in Galapon [Proc. R. Soc. A 473, 20160567 (2017)]. It is shown that, when f(x) does not vanish or has zero of order m at the origin such that (n - m) ≥ 1, the dominant terms of Sn[f] as ω → 0 come from contributions arising from the poles and branch points of the complex valued function f(z)(ω + z)-n. These dominant terms are precisely the terms missed out by naive term by term integration. Furthermore, it is demonstrated how finite-part integration leads to new series representations of special functions by exploiting their known Stieltjes integral representations. Finally, the application of finite part integration in obtaining asymptotic expansions of the effective diffusivity in the limit of high Peclet number, the Green-Kubo formula for the self-diffusion coefficient, and the antisymmetric part of the diffusion tensor in the weak noise limit is discussed.
DEFF Research Database (Denmark)
Bock, Lars Nicolai
2011-01-01
Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi.......Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi....
Energy Technology Data Exchange (ETDEWEB)
LACKS,S.A.
2003-10-09
Transformation, which alters the genetic makeup of an individual, is a concept that intrigues the human imagination. In Streptococcus pneumoniae such transformation was first demonstrated. Perhaps our fascination with genetics derived from our ancestors observing their own progeny, with its retention and assortment of parental traits, but such interest must have been accelerated after the dawn of agriculture. It was in pea plants that Gregor Mendel in the late 1800s examined inherited traits and found them to be determined by physical elements, or genes, passed from parents to progeny. In our day, the material basis of these genetic determinants was revealed to be DNA by the lowly bacteria, in particular, the pneumococcus. For this species, transformation by free DNA is a sexual process that enables cells to sport new combinations of genes and traits. Genetic transformation of the type found in S. pneumoniae occurs naturally in many species of bacteria (70), but, initially only a few other transformable species were found, namely, Haemophilus influenzae, Neisseria meningitides, Neisseria gonorrheae, and Bacillus subtilis (96). Natural transformation, which requires a set of genes evolved for the purpose, contrasts with artificial transformation, which is accomplished by shocking cells either electrically, as in electroporation, or by ionic and temperature shifts. Although such artificial treatments can introduce very small amounts of DNA into virtually any type of cell, the amounts introduced by natural transformation are a million-fold greater, and S. pneumoniae can take up as much as 10% of its cellular DNA content (40).
K-theory for group C*-algebras and semigroup C*-algebras
Cuntz, Joachim; Li, Xin; Yu, Guoliang
2017-01-01
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.
Estimate of the difference between the Kac operator and the Schroedinger semigroup
International Nuclear Information System (INIS)
Ichinose, T.; Satoshi, S.
1997-01-01
An operator norm estimate of the difference between the Kac operator and the Schroedinger semigroup is proved and used to give a variant of the Trotter product formula for Schroedinger operators in the L p operator norm. This extends Helffer's result in the L 2 operator norm to the case in the L p operator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman-Kac a nd Feynman-Kac-Ito formula. (orig.)
Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol
Directory of Open Access Journals (Sweden)
Hong Lai
2012-01-01
Full Text Available We apply semigroup property of enhanced Chebyshev polynomials to present an anonymous authentication protocol. This paper aims at improving security and reducing computational and storage overhead. The proposed scheme not only has much lower computational complexity and cost in the initialization phase but also allows the users to choose their passwords freely. Moreover, it can provide revocation of lost or stolen smart card, which can resist man-in-the-middle attack and off-line dictionary attack together with various known attacks.
Baker, W.R.
1959-08-25
Transformers of a type adapted for use with extreme high power vacuum tubes where current requirements may be of the order of 2,000 to 200,000 amperes are described. The transformer casing has the form of a re-entrant section being extended through an opening in one end of the cylinder to form a coaxial terminal arrangement. A toroidal multi-turn primary winding is disposed within the casing in coaxial relationship therein. In a second embodiment, means are provided for forming the casing as a multi-turn secondary. The transformer is characterized by minimized resistance heating, minimized external magnetic flux, and an economical construction.
Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling
International Nuclear Information System (INIS)
Shikerman, F.; Peer, A.; Horwitz, L. P.
2011-01-01
We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z α ≠z β , and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.
Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling
Energy Technology Data Exchange (ETDEWEB)
Shikerman, F.; Peer, A. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); Horwitz, L. P. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); School of Physics, Tel-Aviv University, Ramat-Aviv 69978 (Israel); Department of Physics, Ariel University Center of Samaria, Ariel 40700 (Israel)
2011-07-15
We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z{sub {alpha}}{ne}z{sub {beta}}, and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.
Energy Technology Data Exchange (ETDEWEB)
Escarela-Perez, R. [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo 180, Col. Reynosa, C.P. 02200, Mexico D.F. (Mexico); Kulkarni, S.V. [Electrical Engineering Department, Indian Institute of Technology, Bombay (India); Melgoza, E. [Instituto Tecnologico de Morelia, Av. Tecnologico 1500, Morelia, Mich., C.P. 58120 (Mexico)
2008-11-15
A six-port impedance network for a three-phase transformer is obtained from a 3D time-harmonic finite-element (FE) model. The network model properly captures the eddy current effects of the transformer tank and frame. All theorems and tools of passive linear networks can be used with the multi-port model to simulate several important operating conditions without resorting anymore to computationally expensive 3D FE simulations. The results of the network model are of the same quality as those produced by the FE program. Although the passive network may seem limited by the assumption of linearity, many important transformer operating conditions imply unsaturated states. Single-phase load-loss measurements are employed to demonstrate the effectiveness of the network model and to understand phenomena that could not be explained with conventional equivalent circuits. In addition, formal deduction of novel closed-form formulae is presented for the calculation of the leakage impedance measured at the high and low voltage sides of the transformer. (author)
Stayton, C Tristan
2009-05-01
Finite element (FE) models are popular tools that allow biologists to analyze the biomechanical behavior of complex anatomical structures. However, the expense and time required to create models from specimens has prevented comparative studies from involving large numbers of species. A new method is presented for transforming existing FE models using geometric morphometric methods. Homologous landmark coordinates are digitized on the FE model and on a target specimen into which the FE model is being transformed. These coordinates are used to create a thin-plate spline function and coefficients, which are then applied to every node in the FE model. This function smoothly interpolates the location of points between landmarks, transforming the geometry of the original model to match the target. This new FE model is then used as input in FE analyses. This procedure is demonstrated with turtle shells: a Glyptemys muhlenbergii model is transformed into Clemmys guttata and Actinemys marmorata models. Models are loaded and the resulting stresses are compared. The validity of the models is tested by crushing actual turtle shells in a materials testing machine and comparing those results to predictions from FE models. General guidelines, cautions, and possibilities for this procedure are also presented.
International Nuclear Information System (INIS)
Upadhyay, M.V.; Van Petegem, S.; Panzner, T.; Lebensohn, R.A.; Van Swygenhoven, H.
2016-01-01
A multi-scale elastic-plastic finite element and fast Fourier transform based approach is proposed to study lattice strain evolution during uniaxial and biaxial loading of stainless steel cruciform shaped samples. At the macroscale, finite element simulations capture the complex coupling between applied forces in the arms and gauge stresses induced by the cruciform geometry. The predicted gauge stresses are used as macroscopic boundary conditions to drive a mesoscale elasto-viscoplastic fast Fourier transform model, from which lattice strains are calculated for particular grain families. The calculated lattice strain evolution matches well with experimental values from in-situ neutron diffraction measurements and demonstrates that the spread in lattice strain evolution between different grain families decreases with increasing biaxial stress ratio. During equibiaxial loading, the model reveals that the lattice strain evolution in all grain families, and not just the 311 grain family, is representative of the polycrystalline response. A detailed quantitative analysis of the 200 and 220 grain family reveals that the contribution of elastic and plastic anisotropy to the lattice strain evolution significantly depends on the applied stress ratio.
Clémence, Alain
2004-01-01
Nous présentons une recherche sur la violence dans le contexte scolaire réalisée en Suisse romande. L'orientation théorique est fondée sur la transformation de la représentation sociale de la violence dans les analyses expertes et ordinaires de l'agression. Différentes définitions de la violence sont discutées dans une perspective développementale de l'identité sociale et des dynamiques des relations scolaires. Les résultats montrent que la représentation de la violence et des actes d'agressi...
Directory of Open Access Journals (Sweden)
Agata Bezubik
2006-03-01
Full Text Available This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.
NATO Advanced Study Institute on Structural Theory of Automata, Semigroups and Universal Algebra
Rosenberg, Ivo; Goldstein, Martin
2005-01-01
Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to contstruct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.
Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming
1990-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
International Nuclear Information System (INIS)
Rund, H.
1984-01-01
A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the 4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a lagrangian be gauge-invariant, uniquely determines the structure of these equations. (author)
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
Boukazouha, F; Poulin-Vittrant, G; Tran-Huu-Hue, L P; Bavencoffe, M; Boubenider, F; Rguiti, M; Lethiecq, M
2015-07-01
This article is dedicated to the study of Piezoelectric Transformers (PTs), which offer promising solutions to the increasing need for integrated power electronics modules within autonomous systems. The advantages offered by such transformers include: immunity to electromagnetic disturbances; ease of miniaturisation for example, using conventional micro fabrication processes; and enhanced performance in terms of voltage gain and power efficiency. Central to the adequate description of such transformers is the need for complex analytical modeling tools, especially if one is attempting to include combined contributions due to (i) mechanical phenomena owing to the different propagation modes which differ at the primary and secondary sides of the PT; and (ii) electrical phenomena such as the voltage gain and power efficiency, which depend on the electrical load. The present work demonstrates an original one-dimensional (1D) analytical model, dedicated to a Rosen-type PT and simulation results are successively compared against that of a three-dimensional (3D) Finite Element Analysis (COMSOL Multiphysics software) and experimental results. The Rosen-type PT studied here is based on a single layer soft PZT (P191) with corresponding dimensions 18 mm × 3 mm × 1.5 mm, which operated at the second harmonic of 176 kHz. Detailed simulational and experimental results show that the presented 1D model predicts experimental measurements to within less than 10% error of the voltage gain at the second and third resonance frequency modes. Adjustment of the analytical model parameters is found to decrease errors relative to experimental voltage gain to within 1%, whilst a 2.5% error on the output admittance magnitude at the second resonance mode were obtained. Relying on the unique assumption of one-dimensionality, the present analytical model appears as a useful tool for Rosen-type PT design and behavior understanding. Copyright © 2015 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Zain-ul-abdein, Muhammad; Nelias, Daniel; Jullien, Jean-Francois; Boitout, Frederic; Dischert, Luc; Noe, Xavier
2011-01-01
Aircraft industry makes extensive use of aluminium alloy AA 6056-T4 in the fabrication of fuselage panels using laser beam welding technique. Since high temperatures are involved in the manufacturing process, the precipitation/dissolution occurrences are expected as solid state phase transformations. These transformations are likely to affect the residual distortion and stress states of the component. The present work investigates the effect of metallurgical phase transformations upon the residual stresses and distortions induced by laser beam welding in a T-joint configuration using the finite element method. Two separate models were studied using different finite element codes, where the first one describes a thermo-mechanical analysis using Abaqus; while the second one discusses a thermo-metallo-mechanical analysis using Sysweld. A comparative analysis of experimentally validated finite element models has been performed and the residual stress states with and without the metallurgical phase transformations are predicted. The results show that the inclusion of phase transformations has a negligible effect on predicted distortions, which are in agreement with the experimental data, but an effect on predicted residual stresses, although the experimentally measured residual stresses are not available to support the analyses.
A Note on the G-Cyclic Operators over a Bounded Semigroup
International Nuclear Information System (INIS)
Hamada, Nuha H.; Jamil, Zeana Z.
2010-08-01
Let H be an infinite-dimensional separable complex Hilbert space, and B(H) be the Banach algebra of all linear bounded operators on H. Let S be a multiplication semigroup of C with 1, an operator T element of B(H) is called G-cyclic operator over S if there is a vector x in H such that {αT n x|α element of S, n ≥ 0} is dense in H. In this case x is called a G-cyclic vector for T over S. If T is G-cyclic operator and S = {1} then T is a hypercyclic operator. In this paper, we study the spectral properties of a G-cyclic operators over a bounded S under the condition that zero is not in the closure of S. We show that the class of all G-cyclic operators is contained in the norm-closure of the class of all hypercyclic operators. (author)
General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2009-01-01
Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172
Observations on finite quantum mechanics
International Nuclear Information System (INIS)
Balian, R.; Itzykson, C.
1986-01-01
We study the canonical transformations of the quantum mechanics on a finite phase space. For simplicity we assume that the configuration variable takes an odd prime number 4 K±1 of distinct values. We show that the canonical group is unitarily implemented. It admits a maximal abelian subgroup of order 4 K, commuting with the finite Fourier transform F, a finite analogue of the harmonic oscillator group. This provides a natural construction of F 1/K and of an orthogonal basis of eigenstates of F [fr
International Nuclear Information System (INIS)
Bartolomaeus, G.; Wilhelm, J.
1983-01-01
Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restriction which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. (author)
Directory of Open Access Journals (Sweden)
Łukasz Rzepnicki
2013-01-01
Full Text Available Small vibrations of a nonhomogeneous string of length one with left end fixed and right one moving with damping are described by the one-dimensional wave equation \\[\\begin{cases} v_{tt}(x,t - \\frac{1}{\\rho}v_{xx}(x,t = 0, x \\in [0,1], t \\in [0, \\infty,\\\\ v(0,t = 0, v_x(1,t + hv_t(1,t = 0, \\\\ v(x,0 = v_0(x, v_t(x,0 = v_1(x,\\end{cases}\\] where \\(\\rho\\ is the density of the string and \\(h\\ is a complex parameter. This equation can be rewritten in an operator form as an abstract Cauchy problem for the closed, densely defined operator B acting on a certain energy space H. It is proven that the operator B generates the exponentially stable \\(C_0\\-semigroup of contractions in the space H under assumptions that \\(\\text{Re}\\; h \\gt 0\\ and the density function is of bounded variation satisfying \\(0 \\lt m \\leq \\rho(x\\ for a.e. \\(x \\in [0, 1]\\.
Spotlight on modern transformer design
Georgilakis, Pavlos S
2009-01-01
Increasing competition in the global transformer market has put tremendous responsibilities on the industry to increase reliability while reducing cost. This book introduces an approach to transformer design using artificial intelligence (AI) techniques in combination with finite element method (FEM).
Sound radiation from finite surfaces
DEFF Research Database (Denmark)
Brunskog, Jonas
2013-01-01
A method to account for the effect of finite size in acoustic power radiation problem of planar surfaces using spatial windowing is developed. Cremer and Heckl presents a very useful formula for the power radiating from a structure using the spatially Fourier transformed velocity, which combined...... with spatially windowing of a plane waves can be used to take into account the finite size. In the present paper, this is developed by means of a radiation impedance for finite surfaces, that is used instead of the radiation impedance for infinite surfaces. In this way, the spatial windowing is included...
Hirschman, Isidore Isaac
2005-01-01
In studies of general operators of the same nature, general convolution transforms are immediately encountered as the objects of inversion. The relation between differential operators and integral transforms is the basic theme of this work, which is geared toward upper-level undergraduates and graduate students. It may be read easily by anyone with a working knowledge of real and complex variable theory. Topics include the finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, and
Directory of Open Access Journals (Sweden)
Liu Min
2010-01-01
Full Text Available In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
International Nuclear Information System (INIS)
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2008-01-01
A new Lagrangian realizing the symmetry of the M-algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian semigroup expansion, a link between the M-algebra and the orthosymplectic algebra osp(32 vertical stroke 1) is established, and an M-algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula. (orig.)
Chen, Shaohua; Xu, Yaopengxiao; Jiao, Yang
2018-06-01
Additive manufacturing such as selective laser sintering and electron beam melting has become a popular technique which enables one to build near-net-shape product from packed powders. The performance and properties of the manufactured product strongly depends on its material microstructure, which is in turn determined by the processing conditions including beam power density, spot size, scanning speed and path etc. In this paper, we develop a computational framework that integrates the finite element method (FEM) and cellular automaton (CA) simulation to model the 3D microstructure of additively manufactured Ti–6Al–4V alloy, focusing on the β → α + β transition pathway in a consolidated alloy region as the power source moves away from this region. Specifically, the transient temperature field resulted from a scanning laser/electron beam following a zig-zag path is first obtained by solving nonlinear heat transfer equations using the FEM. Next, a CA model for the β → α + β phase transformation in the consolidated alloy is developed which explicitly takes into account the temperature dependent heterogeneous nucleation and anisotropic growth of α grains from the parent β phase field. We verify our model by reproducing the overall transition kinetics predicted by the Johnson–Mehl–Avrami–Kolmogorov theory under a typical processing condition and by quantitatively comparing our simulation results with available experimental data. The utility of the model is further demonstrated by generating large-field realistic 3D alloy microstructures for subsequent structure-sensitive micro-mechanical analysis. In addition, we employ our model to generate a wide spectrum of alloy microstructures corresponding to different processing conditions for establishing quantitative process-structure relations for the system.
Stretching and jamming of finite automata
Beijer, de N.; Kourie, D.G.; Watson, B.W.; Cleophas, L.G.W.A.; Watson, B.W.
2004-01-01
In this paper we present two transformations on automata, called stretching and jamming. These transformations will, under certain conditions, reduce the size of the transition table, and under other conditions reduce the string processing time. Given a finite automaton, we can stretch it by
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Locally Finite Root Supersystems
Yousofzadeh, Malihe
2013-01-01
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
International Nuclear Information System (INIS)
Acharya, B.S.; Douglas, M.R.
2006-06-01
We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Transform analysis of generalized functions
Misra, O P
1986-01-01
Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will
Alabdulmohsin, Ibrahim M.
2018-01-01
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Alabdulmohsin, Ibrahim M.
2018-03-07
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Gómez, Fernando
2007-04-01
Reversible evolutions are usually expressed in terms of unitary groups on separable Hilbert spaces, whereas irreversible ones are described by contraction semigroups. In the theory of nonunitary similarity transformations intertwining unitary groups and contraction semigroups, proposed initially in the context of statistical mechanics as part of an exact theory of irreversibility, the unitary groups with such intertwining property have been qualified by the existence of an internal time operator. This work tackles the question of existence of internal time operators for unitary groups with the intertwining property. Equivalent conditions to the existence of internal time operators for such unitary groups are given on the basis of the Sz.-Nagy-Foiaş [Harmonic Analysis of Operators on Hilbert Spaces (North-Holland, Amsterdam, 1970)] dilation theory and the theory of shift invariant subspaces. These conditions permit us to solve the inverse intertwining problem in the negative: there are unitary groups with the intertwining property which do not admit internal time operator. A representative family of such unitary groups is given.
Disc piezoelectric ceramic transformers.
Erhart, Jirií; Půlpán, Petr; Doleček, Roman; Psota, Pavel; Lédl, Vít
2013-08-01
In this contribution, we present our study on disc-shaped and homogeneously poled piezoelectric ceramic transformers working in planar-extensional vibration modes. Transformers are designed with electrodes divided into wedge, axisymmetrical ring-dot, moonie, smile, or yin-yang segments. Transformation ratio, efficiency, and input and output impedances were measured for low-power signals. Transformer efficiency and transformation ratio were measured as a function of frequency and impedance load in the secondary circuit. Optimum impedance for the maximum efficiency has been found. Maximum efficiency and no-load transformation ratio can reach almost 100% and 52 for the fundamental resonance of ring-dot transformers and 98% and 67 for the second resonance of 2-segment wedge transformers. Maximum efficiency was reached at optimum impedance, which is in the range from 500 Ω to 10 kΩ, depending on the electrode pattern and size. Fundamental vibration mode and its overtones were further studied using frequency-modulated digital holographic interferometry and by the finite element method. Complementary information has been obtained by the infrared camera visualization of surface temperature profiles at higher driving power.
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
Measures with locally finite support and spectrum.
Meyer, Yves F
2016-03-22
The goal of this paper is the construction of measures μ on R(n)enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ f μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These unexpected patterns strongly differ from quasicrystals, they provide us with unusual Poisson's formulas, and they might give us an unconventional insight into aperiodic order.
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Supersymmetric theories and finiteness
International Nuclear Information System (INIS)
Helayel-Neto, J.A.
1989-01-01
We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)
Alabdulmohsin, Ibrahim M.
2018-03-07
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Alabdulmohsin, Ibrahim M.
2018-01-01
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Finite fields and applications
Mullen, Gary L
2007-01-01
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...
A summary of maintenance policies for a finite interval
International Nuclear Information System (INIS)
Nakagawa, T.; Mizutani, S.
2009-01-01
It would be an important problem to consider practically some maintenance policies for a finite time span, because the working times of most units are finite in actual fields. This paper converts the usual maintenance models to finite maintenance models. It is more difficult to study theoretically optimal policies for a finite time span than those for an infinite time span. Three usual models of periodic replacement with minimal repair, block replacement and simple replacement are transformed to finite replacement models. Further, optimal periodic and sequential policies for an imperfect preventive maintenance and an inspection model for a finite time span are considered. Optimal policies for each model are analytically derived and are numerically computed
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Phase transition in finite systems
International Nuclear Information System (INIS)
Chomaz, Ph.; Duflot, V.; Duflot, V.; Gulminelli, F.
2000-01-01
In this paper we present a review of selected aspects of Phase transitions in finite systems applied in particular to the liquid-gas phase transition in nuclei. We show that the problem of the non existence of boundary conditions can be solved by introducing a statistical ensemble with an averaged constrained volume. In such an ensemble the microcanonical heat capacity becomes negative in the transition region. We show that the caloric curve explicitly depends on the considered transformation of the volume with the excitation energy and so does not bear direct informations on the characteristics of the phase transition. Conversely, partial energy fluctuations are demonstrated to be a direct measure of the equation of state. Since the heat capacity has a negative branch in the phase transition region, the presence of abnormally large kinetic energy fluctuations is a signal of the liquid gas phase transition. (author)
Quantization and representation theory of finite W algebras
International Nuclear Information System (INIS)
Boer, J. de; Tjin, T.
1993-01-01
In this paper we study the finitely generated algebras underlying W algebras. These so called 'finite W algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of sl 2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite W algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite W symmetry. In the second part we BRST quantize the finite W algebras. The BRST cohomoloy is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite W algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finite W algebras. It is shown, using a quantum inversion of the generalized Miura transformation, that the representations of finite W algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite W algebras. (orig.)
Indian Academy of Sciences (India)
IAS Admin
wavelength, they are called shallow water waves. In the ... Deep and intermediate water waves are dispersive as the velocity of these depends on wavelength. This is not the ..... generation processes, the finite amplitude wave theories are very ...
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
International Nuclear Information System (INIS)
Rittenberg, V.
1983-01-01
Fischer's finite-size scaling describes the cross over from the singular behaviour of thermodynamic quantities at the critical point to the analytic behaviour of the finite system. Recent extensions of the method--transfer matrix technique, and the Hamiltonian formalism--are discussed in this paper. The method is presented, with equations deriving scaling function, critical temperature, and exponent v. As an application of the method, a 3-states Hamiltonian with Z 3 global symmetry is studied. Diagonalization of the Hamiltonian for finite chains allows one to estimate the critical exponents, and also to discover new phase transitions at lower temperatures. The critical points lambda, and indices v estimated for finite-scaling are given
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1983-01-01
Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)
Wang, Victor C. X.; Cranton, Patricia
2011-01-01
The theory of transformative learning has been explored by different theorists and scholars. However, few scholars have made an attempt to make a comparison between transformative learning and Confucianism or between transformative learning and andragogy. The authors of this article address these comparisons to develop new and different insights…
On the asymptotic evolution of finite energy Airy wave functions.
Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S
2015-06-15
In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.
Semigroups of data normalization functions
Warrens, Matthijs J.
2016-01-01
Variable centering and scaling are functions that are typically used in data normalization. Various properties of centering and scaling functions are presented. It is shown that if we use two centering functions (or scaling functions) successively, the result depends on the order in which the
International Nuclear Information System (INIS)
Feinsilver, Philip; Schott, Rene
2009-01-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
Directory of Open Access Journals (Sweden)
D. Naylor
1988-01-01
Full Text Available A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr where r varies over the finite interval (0,a and the order u is taken to be the eigenvalue parameter. When this parameter is large the Bessel function behaves for varying r like the power function ru and by relating the Bessel functions to their corresponding power functions the proof of the inversion formula can be reduced to one depending on the Mellin inversion theorem.
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Finite temperature field theory
Das, Ashok
1997-01-01
This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al
International Nuclear Information System (INIS)
Wachspress, E.
2009-01-01
Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)
Backlund transformations as canonical transformations
International Nuclear Information System (INIS)
Villani, A.; Zimerman, A.H.
1977-01-01
Toda and Wadati as well as Kodama and Wadati have shown that the Backlund transformations, for the exponential lattice equation, sine-Gordon equation, K-dV (Korteweg de Vries) equation and modifies K-dV equation, are canonical transformation. It is shown that the Backlund transformation for the Boussinesq equation, for a generalized K-dV equation, for a model equation for shallow water waves and for the nonlinear Schroedinger equation are also canonical transformations [pt
Compton scattering at finite temperature: thermal field dynamics approach
International Nuclear Information System (INIS)
Juraev, F.I.
2006-01-01
Full text: Compton scattering is a classical problem of quantum electrodynamics and has been studied in its early beginnings. Perturbation theory and Feynman diagram technique enables comprehensive analysis of this problem on the basis of which famous Klein-Nishina formula is obtained [1, 2]. In this work this problem is extended to the case of finite temperature. Finite-temperature effects in Compton scattering is of practical importance for various processes in relativistic thermal plasmas in astrophysics. Recently Compton effect have been explored using closed-time path formalism with temperature corrections estimated [3]. It was found that the thermal cross section can be larger than that for zero-temperature by several orders of magnitude for the high temperature realistic in astrophysics [3]. In our work we use a main tool to account finite-temperature effects, a real-time finite-temperature quantum field theory, so-called thermofield dynamics [4, 5]. Thermofield dynamics is a canonical formalism to explore field-theoretical processes at finite temperature. It consists of two steps, doubling of Fock space and Bogolyubov transformations. Doubling leads to appearing additional degrees of freedom, called tilded operators which together with usual field operators create so-called thermal doublet. Bogolyubov transformations make field operators temperature-dependent. Using this formalism we treat Compton scattering at finite temperature via replacing in transition amplitude zero-temperature propagators by finite-temperature ones. As a result finite-temperature extension of the Klein-Nishina formula is obtained in which differential cross section is represented as a sum of zero-temperature cross section and finite-temperature correction. The obtained result could be useful in quantum electrodynamics of lasers and for relativistic thermal plasma processes in astrophysics where correct account of finite-temperature effects is important. (author)
International Nuclear Information System (INIS)
Meszaros, A.
1984-05-01
In case the graviton has a very small non-zero mass, the existence of six additional massive gravitons with very big masses leads to a finite quantum gravity. There is an acausal behaviour on the scales that is determined by the masses of additional gravitons. (author)
Finite lattice extrapolation algorithms
International Nuclear Information System (INIS)
Henkel, M.; Schuetz, G.
1987-08-01
Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Technische Univ. Muenchen, Garching (Germany). Physik Dept.); Mondragon, M. (Technische Univ. Muenchen, Garching (Germany). Physik Dept.); Zoupanos, G. (National Technical Univ., Athens (Greece). Physics Dept.)
1993-09-01
We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV. (orig.)
International Nuclear Information System (INIS)
Kapetanakis, D.; Mondragon, M.; Zoupanos, G.
1993-01-01
We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV. (orig.)
International Nuclear Information System (INIS)
Kapetanakis, D.; Mondragon, M.
1993-01-01
It is shown how to obtain phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. A very interesting feature of the models with three families is that they predict the top quark mass to be around 178 GeV. 16 refs
Czech Academy of Sciences Publication Activity Database
Šorel, Michal; Šíma, Jiří
2004-01-01
Roč. 62, - (2004), s. 93-110 ISSN 0925-2312 R&D Projects: GA AV ČR IAB2030007; GA MŠk LN00A056 Keywords : radial basis function * neural network * finite automaton * Boolean circuit * computational power Subject RIV: BA - General Mathematics Impact factor: 0.641, year: 2004
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Agaian, Sos; Egiazarian, Karen; Astola, Jaakko
2011-01-01
The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced
Finite element reliability analysis of fatigue life
International Nuclear Information System (INIS)
Harkness, H.H.; Belytschko, T.; Liu, W.K.
1992-01-01
Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)
Strong interaction at finite temperature
Indian Academy of Sciences (India)
Quantum chromodynamics; finite temperature; chiral perturbation theory; QCD sum rules. PACS Nos 11.10. ..... at finite temperature. The self-energy diagrams of figure 2 modify it to ..... method of determination at present. Acknowledgement.
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Oliveira, M.W. de.
1986-01-01
The consequences of the incorporation of finite temperature effects in fields theories are investigated. Particularly, we consider the sypersymmetric non-linear sigma model, calculating the effective potencial in the large N limit. Initially, we present the 1/N expantion formalism and, for the O(N) model of scalar field, we show the impossibility of spontaneous symmetry breaking. Next, we study the same model at finite temperature and in the presence of conserved charges (the O(N) symmetry's generator). We conclude that these conserved charges explicitly break the symmetry. We introduce a calculation method for the thermodynamic potential of the theory in the presence of chemical potentials. We present an introduction to Supersymmetry in the aim of describing some important concepts for the treatment at T>0. We show that Suppersymmetry is broken for any T>0, in opposition to what one expects, by the solution of the Hierachy Problem. (author) [pt
Finite field-dependent symmetries in perturbative quantum gravity
International Nuclear Information System (INIS)
Upadhyay, Sudhaker
2014-01-01
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also
DEFF Research Database (Denmark)
Pedersen, Pia
2012-01-01
Transformation, defined as the step of extracting, arranging and simplifying data into visual form (M. Neurath, 1974), was developed in connection with ISOTYPE (International System Of TYpographic Picture Education) and might well be the most important legacy of Isotype to the field of graphic...... design. Recently transformation has attracted renewed interest because of the book The Transformer written by Robin Kinross and Marie Neurath. My on-going research project, summarized in this paper, identifies and depicts the essential principles of data visualization underlying the process...... of transformation with reference to Marie Neurath’s sketches on the Bilston Project. The material has been collected at the Otto and Marie Neurath Collection housed at the University of Reading, UK. By using data visualization as a research method to look directly into the process of transformation, the project...
De Nicola, Rocco; Fantechi, Alessandro; Gnesi, Stefania; Inverardi, Paola; Nesi, Monica
1991-01-01
In the following a complete set of laws for observational congruence on finite basie LOTOS is listed. This set is not minimal but includes all the laws presented in [2] while for a minimal complete set we refer to [29]. The laws for each operator are grouped together.
Directory of Open Access Journals (Sweden)
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
Belytschko, Ted; Wing, Kam Liu
1987-01-01
In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.
Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.
Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung
2018-01-01
A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.
Excitation spectrum and staggering transformations in lattice quantum models.
Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo
2002-08-01
We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
National Research Council Canada - National Science Library
Metz, Steven
2003-01-01
... adjustment. With American military forces engaged around the world in both combat and stabilization operations, the need for rigorous and critical analysis of security transformation has never been greater...
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
DEFF Research Database (Denmark)
Munck Petersen, Rikke
2005-01-01
Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den.......Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den....
Kisil, Vladimir V.
2010-01-01
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. Covariant transform extends an applicability of the popular wavelets construction to classic examples like the Hardy space H_2, Banach spaces, covariant functional calculus and many others. Keywords: Wavelets, cohe...
Hall, Anndee
2017-01-01
Abstract: Transforming Anatomy Studying historic books allows people to witness the transformation of the world right before their very eyes. The Bruxellensis Icones Anatomicae[1] by Andreas Vesalius is a vital piece of evidence in the movement from a more rudimentary understanding of the human body into the more complex and accurate development of modern anatomy. Vesalius’ research worked to both refute and confirm findings of his predecessor, the great historical Greek philosopher, Galen...
The Use of Finite Fields and Rings to Compute Convolutions
1975-06-06
showed in Ref. 1 that the convolution of two finite sequences of integers (a, ) and (b, ) for k = 1, 2, . . ., d can be obtained as the inverse transform of...since the T.’S are all distinct. Thus T~ exists and (7) can be solved as a = T A the inverse " transform . Next let us impose on (7) the...the inverse transform d-1 Cn= (d) I Cka k=0 If an a can be found so that multiplications by powers of a are simple in hardware, the
Optical Finite Element Processor
Casasent, David; Taylor, Bradley K.
1986-01-01
A new high-accuracy optical linear algebra processor (OLAP) with many advantageous features is described. It achieves floating point accuracy, handles bipolar data by sign-magnitude representation, performs LU decomposition using only one channel, easily partitions and considers data flow. A new application (finite element (FE) structural analysis) for OLAPs is introduced and the results of a case study presented. Error sources in encoded OLAPs are addressed for the first time. Their modeling and simulation are discussed and quantitative data are presented. Dominant error sources and the effects of composite error sources are analyzed.
Anderson, Ian
2011-01-01
Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. ""An excellent text for a topics course in discrete mathematics."" - Bulletin of the Ame
Kalita, Jiten C.; Biswas, Sougata; Panda, Swapnendu
2018-04-01
Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by diagnosing the assumptions of the existing theorems on such vortices. We provide our own set of proofs for establishing the finiteness of the sequence of corner vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a nonzero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. Making use of some elementary concepts of mathematical analysis and our own construction of diametric disks, we conclude that the sequence of corner vortices is finite.
Darboux transformation for the NLS equation
International Nuclear Information System (INIS)
Aktosun, Tuncay; Mee, Cornelis van der
2010-01-01
We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.
DEFF Research Database (Denmark)
Andersen, Nicolai Bo
This paper is about sustainable transformation with a particular focus on listed buildings. It is based on the notion that sustainability is not just a question of energy conditions, but also about the building being robust. Robust architecture means that the building can be maintained and rebuilt......, that it can be adapted to changing functional needs, and that it has an architectural and cultural value. A specific proposal for a transformation that enhances the architectural qualities and building heritage values of an existing building forms the empirical material, which is discussed using different...... theoretical lenses. It is proposed that three parameters concerning the ꞌtransformabilityꞌ of the building can contribute to a more nuanced understanding of sustainable transformation: technical aspects, programmatic requirements and narrative value. It is proposed that the concept of ꞌsustainable...
DEFF Research Database (Denmark)
Neergaard, Helle; Robinson, Sarah; Jones, Sally
, as well as the resources they have when they come to the classroom. It also incorporates perspectives from (ii) transformational learning and explores the concept of (iii) nudging from a pedagogical viewpoint, proposing it as an important tool in entrepreneurship education. The study incorporates......This paper develops the concept of ‘pedagogical nudging’ and examines four interventions in an entrepreneurship classroom and the potential it has for student identity transformation. Pedagogical nudging is positioned as a tool, which in the hands of a reflective, professional......) assists students in straddling the divide between identities, the emotions and tensions this elicits, and (iv) transform student understanding. We extend nudging theory into a new territory. Pedagogical nudging techniques may be able to unlock doors and bring our students beyond the unacknowledged...
The structure of the Hamiltonian in a finite-dimensional formalism based on Weyl's quantum mechanics
International Nuclear Information System (INIS)
Santhanam, T.S.; Madivanane, S.
1982-01-01
Any discussion on finite-dimensional formulation of quantum mechanics involves the Sylvester matrix (finite Fourier transform). In the usual formulation, a remarkable relation exists that gives the Fourier transform as the exponential of the Hamiltonian of a simple harmonic oscillator. In this paper, assuming that such a relation holds also in the finite dimensional case, we extract the logarithm of the Sylvester matrix and in some cases this can be interpreted as the Hamiltonian of the truncated oscillator. We calculate the Hamiltonian matrix explicitly for some special cases of n = 3,4. (author)
The Determining Finite Automata Process
Directory of Open Access Journals (Sweden)
M. S. Vinogradova
2017-01-01
Full Text Available The theory of formal languages widely uses finite state automata both in implementation of automata-based approach to programming, and in synthesis of logical control algorithms.To ensure unambiguous operation of the algorithms, the synthesized finite state automata must be deterministic. Within the approach to the synthesis of the mobile robot controls, for example, based on the theory of formal languages, there are problems concerning the construction of various finite automata, but such finite automata, as a rule, will not be deterministic. The algorithm of determinization can be applied to the finite automata, as specified, in various ways. The basic ideas of the algorithm of determinization can be most simply explained using the representations of a finite automaton in the form of a weighted directed graph.The paper deals with finite automata represented as weighted directed graphs, and discusses in detail the procedure for determining the finite automata represented in this way. Gives a detailed description of the algorithm for determining finite automata. A large number of examples illustrate a capability of the determinization algorithm.
Finite energy electroweak dyon
Energy Technology Data Exchange (ETDEWEB)
Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, College of Natural Sciences, Seoul (Korea, Republic of); Cho, Y.M. [Konkuk University, Administration Building 310-4, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of)
2015-02-01
The latest MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss three different ways to estimate the mass of the electroweak monopole. We first present the dimensional and scaling arguments which indicate the monopole mass to be around 4 to 10 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strength at short distance. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC. (orig.)
Probabilistic fracture finite elements
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-05-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
International Nuclear Information System (INIS)
Tonks, M.R.; Williamson, R.; Masson, R.
2015-01-01
The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. While FEM is commonly used to solve solid mechanics equations, it can be applied to a large range of BVPs from many different fields. FEM has been used for reactor fuels modelling for many years. It is most often used for fuel performance modelling at the pellet and pin scale, however, it has also been used to investigate properties of the fuel material, such as thermal conductivity and fission gas release. Recently, the United Stated Department Nuclear Energy Advanced Modelling and Simulation Program has begun using FEM as the basis of the MOOSE-BISON-MARMOT Project that is developing a multi-dimensional, multi-physics fuel performance capability that is massively parallel and will use multi-scale material models to provide a truly predictive modelling capability. (authors)
Description of the electron-hydrogen collision by the Coulomb Fourier transform method
International Nuclear Information System (INIS)
Levin, S.B.
2005-01-01
A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals
Axial anomaly at finite temperature and finite density
International Nuclear Information System (INIS)
Qian Zhixin; Su Rukeng; Yu, P.K.N.
1994-01-01
The U(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed. (orig.)
DEFF Research Database (Denmark)
Andersen, Nicolai Bo
This paper is about sustainable transformation with a particular focus on listed buildings. It is based on the notion that sustainability is not just a question of energy conditions, but also about the building being robust. Robust architecture means that the building can be maintained and rebuil...
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2008-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2010-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
International Nuclear Information System (INIS)
Murphy, J.H.
1982-01-01
A superconducting transformer having a winding arrangement that provides for current limitation when subjected to a current transient as well as more efficient utilization of radial spacing and winding insulation. Structural innovations disclosed include compressed conical shaped winding layers and a resistive matrix to promote rapid switching of current between parallel windings
Transformation & Metamorphosis
Lott, Debra
2009-01-01
The sculptures of Canadian artist Brian Jungen are a great inspiration for a lesson on creating new forms. Jungen transforms found objects into unique creations without fully concealing their original form or purpose. Frank Stella's sculpture series, including "K.132,2007" made of stainless steel and spray paint, is another great example of…
DEFF Research Database (Denmark)
Enemark, Stig; Dahl Højgaard, Pia
2017-01-01
, was a result of transforming society from a feudal system to a capitalistic and market based economy. This story is interesting in itself - but it also provides a key to understanding the cadastral system of today. The system has evolved over time and now serves a whole range of functions in society. The paper...
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one
Universal conditions for finite renormalizable quantum field theories
International Nuclear Information System (INIS)
Kranner, G.
1990-10-01
Analyzing general renormalization constants in covariant gauge and minimal subtraction, we consider universal conditions for cancelling UV-divergences in renormalizable field theories with simple gauge groups, and give constructive methods for finding nonsupersymmetric finite models. The divergent parts of the renormalization constants for fields explicitly depend on the gauge parameter ξ. Finite theories simply need finite couplings. We show that respective FinitenessConditions imply a hierarchy, the center of which are the FCs for the gauge coupling g and the Yukawa couplings of the massless theory. To gain more information about F we analyze the Yukawa-FC in greater detail. Doing so algebraically, we find out and fix all inner symmetries. Additionally, Yuakawa-couplings must be invariant under gauge transformation. Then it becomes extremely difficult to obey a FC, yield rational numbers for F ∼ 1, and satisfy the factorization-condition, unless F = 1. The particular structure of the F = 1-system allows for a most general ansatz. We figure out the simplest case, getting precisely just couplings and particle content of a general N=1-supersymmetric theory. We list a class of roughly 4000 types of theories, containing all supersymmetric, completely finite, and many more finite theories as well. (Author, shortened by Quittner) 11 figs., 54 refs
Finite-mode analysis by means of intensity information in fractional optical systems
Alieva, T.; Bastiaans, M.J.
2002-01-01
It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes, can be reconstructed from the knowledge of its Radon-Wigner transform -- associated with the intensity distribution in a fractional Fourier transform optical system -- at only two transversal points.
Energy Technology Data Exchange (ETDEWEB)
Ripamonti, G.
1987-10-01
The optimum turn-ratio of transformers used for coupling large capacitance detectors to amplifiers is demonstrated to be dependent on the actual weighting function of the following shaper. As an example, the optimum finite cusp shaping with a flat top is considered. For this case, the optimum turn-ratio is found to be dependent on the flat top duration. As finite magnetizing inductance in real transformers produces diverging noise with unipolar shaping, flat-top tripolar zero-area shapers are also considered.
Axial anomaly at finite temperature
International Nuclear Information System (INIS)
Chaturvedi, S.; Gupte, Neelima; Srinivasan, V.
1985-01-01
The Jackiw-Bardeen-Adler anomaly for QED 4 and QED 2 are calculated at finite temperature. It is found that the anomaly is independent of temperature. Ishikawa's method [1984, Phys. Rev. Lett. vol. 53 1615] for calculating the quantised Hall effect is extended to finite temperature. (author)
Finite flavour groups of fermions
International Nuclear Information System (INIS)
Grimus, Walter; Ludl, Patrick Otto
2012-01-01
We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Although in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects. (topical review)
On finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1984-01-01
The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Massively Parallel Finite Element Programming
Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang
2010-01-01
Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Regularization of EIT reconstruction based on multi-scales wavelet transforms
Directory of Open Access Journals (Sweden)
Gong Bo
2016-09-01
Full Text Available Electrical Impedance Tomography (EIT intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
International Nuclear Information System (INIS)
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
Mimetic finite difference method
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Directory of Open Access Journals (Sweden)
Felician ALECU
2012-04-01
Full Text Available XSLT style sheets are designed to transform the XML documents into something else. The two most popular parsers of the moment are the Document Object Model (DOM and the Simple API for XML (SAX. DOM is an official recommendation of the W3C (available at http://www.w3.org/TR/REC-DOM-Level-1, while SAX is a de facto standard. A good parser should be fast, space efficient, rich in functionality and easy to use.
Smith, James L.; Helenberg, Harold W.; Kilsdonk, Dennis J.
1979-01-01
There is provided an improved RF transformer having a single-turn secondary of cylindrical shape and a coiled encapsulated primary contained within the secondary. The coil is tapered so that the narrowest separation between the primary and the secondary is at one end of the coil. The encapsulated primary is removable from the secondary so that a variety of different capacity primaries can be utilized with one secondary.
DEFF Research Database (Denmark)
Majgaard, Klaus
The purpose of this paper is to enhance the conceptual understanding of the mediatory relationship between paradoxes on an organizational and an individual level. It presents a concept of agency that comprises and mediates between a structural and individual pole. The constitution of this agency ...... is achieved through narrative activity that oscillates between the poles and transforms paradoxes through the configuration of plots and metaphors. Empirical cases are introduced in order to illustrate the implications of this understanding....
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
On the spectral properties of random finite difference operators
International Nuclear Information System (INIS)
Kunz, H.; Souillard, B.
1980-01-01
We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Testing Linear Temporal Logic Formulae on Finite Execution Traces
Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)
2001-01-01
We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.
Electrical transformer handbook
Energy Technology Data Exchange (ETDEWEB)
Hurst, R.W.; Horne, D. (eds.)
2005-07-01
This handbook is a valuable user guide intended for electrical engineering and maintenance personnel, electrical contractors and electrical engineering students. It provides current information on techniques and technologies that can help extend the life of transformers. It discusses transformer testing, monitoring, design, commissioning, retrofitting and other elements involved in keeping electrical transformers in safe and efficient operation. It demonstrates how a power transformer can be put to use and common problems faced by owners. In addition to covering control techniques, testing and maintenance procedures, this handbook covers the power transformer; control electrical power transformer; electrical power transformer; electrical theory transformer; used electrical transformer; down electrical step transformer; electrical manufacturer transformer; electrical picture transformer; electrical transformer work; electrical surplus transformer; current transformer; step down transformer; voltage transformer; step up transformer; isolation transformer; low voltage transformer; toroidal transformer; high voltage transformer; and control power transformer. The handbook includes articles from leading experts on overcurrent protection of transformers; ventilated dry-type transformers; metered load factors for low-voltage, and dry-type transformers in buildings. The maintenance of both dry-type or oil-filled transformers was discussed with reference to sealing, gaskets, oils, moisture and testing. The adoption of dynamic load practices was also discussed along with the reclamation or recycling of used lube oil, transformer dielectric fluids and aged solid insulation. A buyer's guide and directory of transformer manufacturers and suppliers was also included. refs., tabs., figs.
Modelling of stresses generated in steels by phase transformations
International Nuclear Information System (INIS)
Dudek, K.; Glowacki, M.; Pietrzyk, M.
1999-01-01
Numerical model describing stresses arising during phase transformations in steels products is presented. The full model consists of three components. The first component uses finite element solution of Fourier equation for an evaluation of the temperature field inside the sample. The second component predicts kinetics of phase transformation occurring during cooling of steel products. Coupling of these two components allows prediction of structure and properties of final products at room temperature. The third component uses elastic-plastic finite element model for prediction of stresses caused by non-uniform temperatures and by changes of volume during transformations. Typical results of simulations performed for cooling of rails after hot rolling are presented. (author)
Finite spatial volume approach to finite temperature field theory
International Nuclear Information System (INIS)
Weiss, Nathan
1981-01-01
A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)
Automatic Construction of Finite Algebras
Institute of Scientific and Technical Information of China (English)
张健
1995-01-01
This paper deals with model generation for equational theories,i.e.,automatically generating (finite)models of a given set of (logical) equations.Our method of finite model generation and a tool for automatic construction of finite algebras is described.Some examples are given to show the applications of our program.We argue that,the combination of model generators and theorem provers enables us to get a better understanding of logical theories.A brief comparison betwween our tool and other similar tools is also presented.
Photon propagators at finite temperature
International Nuclear Information System (INIS)
Yee, J.H.
1982-07-01
We have used the real time formalism to compute the one-loop finite temperature corrections to the photon self energies in spinor and scalar QED. We show that, for a real photon, only the transverse components develop the temperature-dependent masses, while, for an external static electromagnetic field applied to the finite temperature system, only the static electric field is screened by thermal fluctuations. After showing how to compute systematically the imaginary parts of the finite temperature Green functions, we have attempted to give a microscopic interpretation of the imaginary parts of the self energies. (author)
Usher, P. D.
1997-12-01
William Shakespeare's Hamlet has much evidence to suggest that the Bard was aware of the cosmological models of his time, specifically the geocentric bounded Ptolemaic and Tychonic models, and the infinite Diggesian. Moreover, Shakespeare describes how the Ptolemaic model is to be transformed to the Diggesian. Hamlet's "transformation" is the reason that Claudius, who personifies the Ptolemaic model, summons Rosencrantz and Guildenstern, who personify the Tychonic. Pantometria, written by Leonard Digges and his son Thomas in 1571, contains the first technical use of the word "transformation." At age thirty, Thomas Digges went on to propose his Perfit Description, as alluded to in Act Five where Hamlet's age is given as thirty. In Act Five as well, the words "bore" and "arms" refer to Thomas' vocation as muster-master and his scientific interest in ballistics. England's leading astronomer was also the father of the poet whose encomium introduced the First Folio of 1623. His oldest child Dudley became a member of the Virginia Company and facilitated the writing of The Tempest. Taken as a whole, such manifold connections to Thomas Digges support Hotson's contention that Shakespeare knew the Digges family. Rosencrantz and Guildenstern in Hamlet bear Danish names because they personify the Danish model, while the king's name is latinized like that of Claudius Ptolemaeus. The reason Shakespeare anglicized "Amleth" to "Hamlet" was because he saw a parallel between Book Three of Saxo Grammaticus and the eventual triumph of the Diggesian model. But Shakespeare eschewed Book Four, creating this particular ending from an infinity of other possibilities because it "suited his purpose," viz. to celebrate the concept of a boundless universe of stars like the Sun.
Wolfgang, F.; Nicol, J.
1962-11-01
Transformer apparatus is designed for measuring the amount of a paramagnetic substance dissolved or suspended in a diamagnetic liquid. The apparatus consists of a cluster of tubes, some of which are closed and have sealed within the diamagnetic substance without any of the paramagnetic material. The remaining tubes are open to flow of the mix- ture. Primary and secondary conductors are wrapped around the tubes in such a way as to cancel noise components and also to produce a differential signal on the secondaries based upon variations of the content of the paramagnetic material. (AEC)
McLyman, Colonel Wm. T.
1996-01-01
None given. From first Par: Many spacecraft (S/C) and surface rovers require the transfer of signals and power across rotating interfaces. Science instruments, antennas and solar arrays are elements needing rotary power transfer for certain (S/C) configurations. Delivery of signal and power has mainly been done by using the simplest means, the slip ring approach. This approach, although simple, leaves debris generating noise over a period of time...The rotary transformer is a good alternative to slip rings for signal and power transfer.
Finite-amplitude, pulsed, ultrasonic beams
Coulouvrat, François; Frøysa, Kjell-Eivind
An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.
Signal detection without finite-energy limits to quantum resolution
Luis Aina, Alfredo
2013-01-01
We show that there are extremely simple signal detection schemes where the finiteness of energy resources places no limit on the resolution. On the contrary, larger resolution can be obtained with lower energy. To this end the generator of the signal-dependent transformation encoding the signal information on the probe state must be different from the energy. We show that the larger the deviation of the probe state from being the minimum-uncertainty state, the better the resolution.
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
Finite element computational fluid mechanics
International Nuclear Information System (INIS)
Baker, A.J.
1983-01-01
This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows
Unified derivation of the Galileo and the Lorentz transformations
International Nuclear Information System (INIS)
Sardelis, D.A.
1982-01-01
By using the principle of relativity together with the general assumptions of space-time homogeneity and space isotropy underlying the principle of inertia, a most general transformation is constructed connecting any two inertial frames. The Galileo and the Lorentz transformations are then deduced by constraining these general inertial transformations through the corresponding two physical principles: the (classical) principle of acceleration invariance and the (relativistic) principle that all interactions propagate with the same finite and invariant speed. (author)
Design of an optical spatial interferometer with transformation optics
International Nuclear Information System (INIS)
Naghibi, Atefeh; Shokooh-Saremi, Mehrdad
2015-01-01
In this paper, we apply transformation optics to design an optical spatial interferometer. The transformation equations are described and two-dimensional finite element simulations are presented to numerically confirm the functionality of the device. It is shown that a small change in the refractive index can alter the interference pattern and hence can be detected. The design of the interferometer could expand transformation optics’ applications and make way for introduction of new structures with unique electromagnetic or optical functionalities. (paper)
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Finite Size Scaling of Perceptron
Korutcheva, Elka; Tonchev, N.
2000-01-01
We study the first-order transition in the model of a simple perceptron with continuous weights and large, bit finite value of the inputs. Making the analogy with the usual finite-size physical systems, we calculate the shift and the rounding exponents near the transition point. In the case of a general perceptron with larger variety of inputs, the analysis only gives bounds for the exponents.
Incompleteness in the finite domain
Czech Academy of Sciences Publication Activity Database
Pudlák, Pavel
2017-01-01
Roč. 23, č. 4 (2017), s. 405-441 ISSN 1079-8986 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : finite domain Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.742, year: 2016 https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/incompleteness-in-the-finite-domain/D239B1761A73DCA534A4805A76D81C76
Symbolic computation with finite biquandles
Creel, Conrad; Nelson, Sam
2007-01-01
A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Z_p from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
The principle of finiteness – a guideline for physical laws
International Nuclear Information System (INIS)
Sternlieb, Abraham
2013-01-01
I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.
Hierarchical coarse-graining transform.
Pancaldi, Vera; King, Peter R; Christensen, Kim
2009-03-01
We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.
International Nuclear Information System (INIS)
Beer, G.
2003-01-01
State forestry company Lesy, s.p., Banska Bystrica have chosen Austrian state forestry company to operate as their restructuring advisor. 20 million Sk (0.142 mn Euro) were assigned to transformation of Lesy SR from a state enterprise to a state-owned joint-stock company. The whole process should take two years. The joint-stock company should be established at the beginning of next year. 'What we have to do first is to define the objectives and perspectives of this restructuring,' claims new director, Karol Vins. The new boss recalled all directors of the 26 branches. They were given a lot of freedom to trade with wood. The new management wants to establish a profit-making company. At the moment the company has total claims of 600 million Sk (14.59 million Eur) it will have to provision for
Jones, Patricia S; Zhang, Xinwei Esther; Meleis, Afaf I
2003-11-01
Asian American immigrant women engaged in filial caregiving are at special risk for health problems due to complex contextual factors related to immigration, cultural traditions, and role transition. This study examines the experience of two groups of immigrant Asian American women who are caring for older parents. A total of 41 women (22 Chinese American and 19 Filipino American) were interviewed in a study based on Strauss and Corbin's grounded theory methodology. The women were determined to be loyal to their traditional culture, which included strong filial values, while adapting to a new culture. Through the struggle of meeting role expectations and coping with paradox, the women mobilized personal and family resources to transform vulnerability into strength and well-being.
Rutherford, Ernest
2012-01-01
Radioactive Transformations describes Ernest Rutherford's Nobel Prize-winning investigations into the mysteries of radioactive matter. In this historic work, Rutherford outlines the scientific investigations that led to and coincided with his own research--including the work of Wilhelm Rӧntgen, J. J. Thomson, and Marie Curie--and explains in detail the experiments that provided a glimpse at special relativity, quantum mechanics, and other concepts that would shape modern physics. This new edition features a comprehensive introduction by Nobel Laureate Frank Wilczek which engagingly explains how Rutherford's early research led to a better understanding of topics as diverse as the workings of the atom's nucleus, the age of our planet, and the fusion in stars.
International Nuclear Information System (INIS)
Iwasaki, Hiroshi; Ohshima, Ken-ichi
2011-01-01
The 11th lecture about microstructures and fluctuation in solids reports on the martensitic phase transformation of alkali metals and alloys. The martensitic transformation is a diffusionless first order phase transformation. Martensitic transformations are classified into two with respect to kinetics, one is isothermal transformation and the other is athermal transformation. The former transformation depends upon both temperature and time, but the latter solely depends on temperature. The former does not have a definite transformation start temperature but occurs after some finite incubation time during isothermal holding. The isothermal martensitic transformation is changed to the athermal one under high magnetic field, and also the reverse transformation occurs under the application of hydrostatic pressure. The former phenomena were observed in Fe-Ni-Mn alloys, Fe-Ni-Cr alloys and also the reverse transformation in Fe-3.1at%Ni-0.5at%Mn alloys. The athermal transformation was observed in Li and Na metals at 73 and 36 K, respectively. A neutron diffraction study has been performed on single crystals of metallic Na. On cooling the virgin sample, the incubation time to transform from the bcc structure to the low-temperature structure (9R structure) is formed to be more than 2h at 38 K, 2 K higher than the transformation temperature of 36 K. The full width of half maximum of the Bragg reflection suddenly increased, due to some deformation introduced by the nucleation of the low-temperature structure. In relation to the deformation, strong extra-diffuse scattering (Huang scattering) was observed around the Bragg reflection in addition to thermal diffuse scattering. The kinetics of the martensitic transformation in In-Tl alloys has been studied by x-ray and neutron diffraction methods. A characteristic incubation time appeared at fixed temperature above Ms, the normal martensitic transformation start temperature. (author)
Exactly solvable models: the way towards a rigorous treatment of phase transitions in finite systems
International Nuclear Information System (INIS)
Bugaev, K.A.
2007-01-01
The exact analytical solutions of a variety of statistical models recently obtained for finite systems are thoroughly discussed. Among them are a constrained version of the statistical multifragmentation model, the Bag Model of Gases and the Hills and Dales Model of surface partition. The finite volume analytical solutions of these models were obtained by a novel powerful mathematical method - the Laplace-Fourier transform. The Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark-gluon plasma and the surface entropy of large clusters on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows one to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics [ru
Finiteness of quantum field theories and supersymmetry
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)
On the boundary of the group of transformations leaving a measure quasi-invariant
Energy Technology Data Exchange (ETDEWEB)
Neretin, Yu A [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2013-08-31
Let A be a Lebesgue measure space. We interpret measures on A×A×R{sup ×} as 'maps' from A to A, which 'spread' A along itself; their Radon-Nikodym derivatives are also spread. We discuss the basic properties of the semigroup of such maps and the action of this semigroup on the spaces L{sup p}(A). Bibliography: 26 titles.
Toward finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1986-01-01
The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)
Dual and primal mixed Petrov-Galerkin finite element methods in heat transfer problems
International Nuclear Information System (INIS)
Loula, A.F.D.; Toledo, E.M.
1988-12-01
New mixed finite element formulations for the steady state heat transfer problem are presented with no limitation in the choice of conforming finite element spaces. Adding least square residual forms of the governing equations of the classical Galerkin formulation the original saddle point problem is transformed into a minimization problem. Stability analysis, error estimates and numerical results are presented, confirming the error estimates and the good performance of this new formulation. (author) [pt
The Laguerre finite difference one-way equation solver
Terekhov, Andrew V.
2017-05-01
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.
On characters of finite groups
Broué, Michel
2017-01-01
This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).
Finite and profinite quantum systems
Vourdas, Apostolos
2017-01-01
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
Global finite-time attitude stabilization for rigid spacecraft in the exponential coordinates
Shi, Xiao-Ning; Zhou, Zhi-Gang; Zhou, Di
2018-06-01
This paper addresses the global finite-time attitude stabilisation problem on the special orthogonal group (SO(3)) for a rigid spacecraft via homogeneous feedback approach. Considering the topological and geometric properties of SO(3), the logarithm map is utilised to transform the stabilisation problem on SO(3) into the one on its associated Lie algebra (?). A model-independent discontinuous state feedback plus dynamics compensation scheme is constructed to achieve the global finite-time attitude stabilisation in a coordinate-invariant way. In addition, to address the absence of angular velocity measurements, a sliding mode observer is proposed to reconstruct the unknown angular velocity information within finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed finite-time controllers.
Calculation of reactivity using a finite impulse response filter
Energy Technology Data Exchange (ETDEWEB)
Suescun Diaz, Daniel [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil); Senra Martinez, Aquilino [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil)], E-mail: aquilino@lmp.ufrj.br; Carvalho Da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil)
2008-03-15
A new formulation is presented in this paper to solve the inverse kinetics equation. This method is based on the Laplace transform of the point kinetics equations, resulting in an expression equivalent to the inverse kinetics equation as a function of the power history. Reactivity can be written in terms of the summation of convolution with response to impulse, characteristic of a linear system. For its digital form the Z-transform is used, which is the discrete version of the Laplace transform. This new method of reactivity calculation has very special features, amongst which it can be pointed out that the linear part is characterized by a filter named finite impulse response (FIR). The FIR filter will always be, stable and non-varying in time, and, apart from this, it can be implemented in the non-recursive form. This type of implementation does not require feedback, allowing the calculation of reactivity in a continuous way.
Finite element analysis of a finite-strain plasticity problem
International Nuclear Information System (INIS)
Crose, J.G.; Fong, H.H.
1984-01-01
A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Variational collocation on finite intervals
International Nuclear Information System (INIS)
Amore, Paolo; Cervantes, Mayra; Fernandez, Francisco M
2007-01-01
In this paper, we study a set of functions, defined on an interval of finite width, which are orthogonal and which reduce to the sinc functions when the appropriate limit is taken. We show that these functions can be used within a variational approach to obtain accurate results for a variety of problems. We have applied them to the interpolation of functions on finite domains and to the solution of the Schroedinger equation, and we have compared the performance of the present approach with others
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Finite connectivity attractor neural networks
International Nuclear Information System (INIS)
Wemmenhove, B; Coolen, A C C
2003-01-01
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous
Kanter, Rosabeth Moss
2008-01-01
Large corporations have long been seen as lumbering, inflexible, bureaucratic--and clueless about global developments. But recently some multinationals seem to be transforming themselves: They're engaging employees, moving quickly, and introducing innovations that show true connection with the world. Harvard Business School's Kanter ventured with a research team inside a dozen global giants--including IBM, Procter & Gamble, Omron, CEMEX, Cisco, and Banco Real--to discover what has been driving the change. After conducting more than 350 interviews on five continents, she and her colleagues came away with a strong sense that we are witnessing the dawn of a new model of corporate power: The coordination of actions and decisions on the front lines now appears to stem from widely shared values and a sturdy platform of common processes and technology, not from top-down decrees. In particular, the values that engage the passions of far-flung workforces stress openness, inclusion, and making the world a better place. Through this shift in what might be called their guidance systems, the companies have become as creative and nimble as much smaller ones, even while taking on social and environmental challenges of a scale that only large enterprises could attempt. IBM, for instance, has created a nonprofit partnership, World Community Grid, through which any organization or individual can donate unused computing power to research projects and see what is being done with the donation in real time. IBM has gained an inspiring showcase for its new technology, helped business partners connect with the company in a positive way, and offered individuals all over the globe the chance to contribute to something big.
Ancilla-approximable quantum state transformations
Energy Technology Data Exchange (ETDEWEB)
Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)
2015-04-15
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.
Ancilla-approximable quantum state transformations
International Nuclear Information System (INIS)
Blass, Andreas; Gurevich, Yuri
2015-01-01
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation
Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains
International Nuclear Information System (INIS)
Ferraro, N.M.; Jardin, S.C.; Luo, X.
2010-01-01
The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.
Multiscale Finite Element Methods for Flows on Rough Surfaces
Efendiev, Yalchin
2013-01-01
In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.
Finite element calculation of the interaction energy of shape memory alloy
International Nuclear Information System (INIS)
Yang, Seung Yong
2004-01-01
Strain energy due to the mechanical interaction between self-accommodation groups of martensitic phase transformation is called interaction energy. Evaluation of the interaction energy should be accurate since the energy appears in constitutive models for predicting the mechanical behavior of shape memory alloy. In this paper, the interaction energy is evaluated in terms of theoretical formulation and explicit finite element calculation. A simple example with two habit plane variants was considered. It was shown that the theoretical formulation assuming elastic interaction between the self-accommodation group and matrix gives larger interaction energy than explicit finite element calculation in which transformation softening is accounted for
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Numerical calculation of the Fresnel transform.
Kelly, Damien P
2014-04-01
In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Dilatation transformation in the string model
Energy Technology Data Exchange (ETDEWEB)
Chikashige, Y [Tokyo Univ. (Japan). Coll. of General Education; Hosoda, M; Saito, S
1975-05-01
Dilatation transformation is discussed in the string model. We show that it becomes meaningful in the infinite slope limit of Regge trajectories for the motion of a free string. It turns out to be equivalent to the high energy limit of the dual amplitudes, with the Regge slope kept finite, in the case of interacting strings. The scaling phenomenon is explained from this point of view.
Application of Laplace transform to industrial problems
International Nuclear Information System (INIS)
Dubois, D.J.M.; Vagner, J.
1989-01-01
This paper presents two industrial applications of a new methodology based on Laplace transform properties which has been implemented in an industrial finite element program. In structures endowed with thermal and mechanical properties constant with the temperature, the stresses are computed for unit thermal shocks applied on the areas which are actually affected by the temperature variations. The analytical formulation and the general feature of this implementation are presented
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
International Nuclear Information System (INIS)
Bovier, A.; Lueling, M.; Wyler, D.
1980-12-01
We present a new class of finite subgroups of SU(3) of the form Zsub(m) s zsub(n) (semidirect product). We also apply the methods used to investigate semidirect products to the known SU(3) subgroups Δ(3n 2 ) and Δ(6n 2 ) and give analytic formulae for representations (characters) and Clebsch-Gordan coefficients. (orig.)
On symmetric pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal
2004-01-01
Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004
Finite length Taylor Couette flow
Streett, C. L.; Hussaini, M. Y.
1987-01-01
Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.
Finite-temperature confinement transitions
International Nuclear Information System (INIS)
Svetitsky, B.
1984-01-01
The formalism of lattice gauge theory at finite temperature is introduced. The framework of universality predictions for critical behavior is outlined, and recent analytic work in this direction is reviewed. New Monte Carlo information for the SU(4) theory are represented, and possible results of the inclusion of fermions in the SU(3) theory are listed
Ward identities at finite temperature
International Nuclear Information System (INIS)
DOlivo, J.C.; Torres, M.; Tututi, E.
1996-01-01
The Ward identities for QED at finite temperature are derived using the functional real-time formalism. They are verified by an explicit one-loop calculation. An effective causal vertex is constructed which satisfy the Ward identity with the associated retarded self-energy. copyright 1996 American Institute of Physics
Finite-Temperature Higgs Potentials
International Nuclear Information System (INIS)
Dolgopolov, M.V.; Gurskaya, A.V.; Rykova, E.N.
2016-01-01
In the present article we consider the short description of the “Finite-Temperature Higgs Potentials” program for calculating loop integrals at vanishing external momenta and applications for extended Higgs potentials reconstructions. Here we collect the analytic forms of the relevant loop integrals for our work in reconstruction of the effective Higgs potential parameters in extended models (MSSM, NMSSM and etc.)
Development and verification of printed circuit board toroidal transformer model
DEFF Research Database (Denmark)
Pejtersen, Jens; Mønster, Jakob Døllner; Knott, Arnold
2013-01-01
An analytical model of an air core printed circuit board embedded toroidal transformer configuration is presented. The transformer has been developed for galvanic isolation of very high frequency switch-mode dc-dc power converter applications. The theoretical model is developed and verified...... by comparing calculated parameters with 3D finite element simulations and experimental measurement results. The developed transformer model shows good agreement with the simulated and measured results. The model can be used to predict the parameters of printed circuit board toroidal transformer configurations...
Transformer Protection Using the Wavelet Transform
ÖZGÖNENEL, Okan; ÖNBİLGİN, Güven; KOCAMAN, Çağrı
2014-01-01
This paper introduces a novel approach for power transformer protection algorithm. Power system signals such as current and voltage have traditionally been analysed by the Fast Fourier Transform. This paper aims to prove that the Wavelet Transform is a reliable and computationally efficient tool for distinguishing between the inrush currents and fault currents. The simulated results presented clearly show that the proposed technique for power transformer protection facilitates the a...
The Bargmann transform and canonical transformations
International Nuclear Information System (INIS)
Villegas-Blas, Carlos
2002-01-01
This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480-5505 (1995)]--when the configuration space is the two-sphere S 2 and for a Bargmann transform that we introduce for the three-sphere S 3 . It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C 3 or C 4 . We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141-1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145-205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L 2 (S 2 ) or L 2 (S 3 ), we show finally that the studied Bargmann transforms are actually coherent states transforms
Introduction to finite temperature and finite density QCD
International Nuclear Information System (INIS)
Kitazawa, Masakiyo
2014-01-01
It has been pointed out that QCD (Quantum Chromodynamics) in the circumstances of medium at finite temperature and density shows numbers of phenomena similar to the characteristics of solid state physics, e.g. phase transitions. In the past ten years, the very high temperature and density matter came to be observed experimentally at the heavy ion collisions. At the same time, the numerical QCD analysis at finite temperature and density attained quantitative level analysis possible owing to the remarkable progress of computers. In this summer school lecture, it has been set out to give not only the recent results, but also the spontaneous breaking of the chiral symmetry, the fundamental theory of finite temperature and further expositions as in the following four sections. The first section is titled as 'Introduction to Finite Temperature and Density QCD' with subsections of 1.1 standard model and QCD, 1.2 phase transition and phase structure of QCD, 1.3 lattice QCD and thermodynamic quantity, 1.4 heavy ion collision experiments, and 1.5 neutron stars. The second one is 'Equilibrium State' with subsections of 2.1 chiral symmetry, 2.2 vacuum state: BCS theory, 2.3 NJL (Nambu-Jona-Lasinio) model, and 2.4 color superconductivity. The third one is 'Static fluctuations' with subsections of 3.1 fluctuations, 3.2 moment and cumulant, 3.3 increase of fluctuations at critical points, 3.4 analysis of fluctuations by lattice QCD and Taylor expansion, and 3.5 experimental exploration of QCD phase structure. The fourth one is 'Dynamical Structure' with 4.1 linear response theory, 4.2 spectral functions, 4.3 Matsubara function, and 4.4 analyses of dynamical structure by lattice QCD. (S. Funahashi)
Finite-element-analysis of fields radiated from ICRF antenna
International Nuclear Information System (INIS)
Yamanaka, Kaoru; Sugihara, Ryo.
1984-04-01
In several simple geometries, electromagnetic fields radiated from a loop antenna, on which a current oscillately flows across the static magnetic field B-vector 0 , are calculated by the finite element method (FEM) as well as by analytic methods in a cross section of a plasma cylinder. A finite wave number along B-vector 0 is assumed. Good agreement between FEM and the analytic solutions is obtained, which indicates the accuracy of FEM solutions. The method is applied to calculations of fields from a half-turn antenna and reasonable results are obtained. It is found that a straightforward application of FEM to problems in an anisotropic medium may bring about erroneous results and that an appropriate coordinate transformation is needed for FEM to become applicable. (author)
Quantum finite-depth memory channels: Case study
International Nuclear Information System (INIS)
Rybar, Tomas; Ziman, Mario
2009-01-01
We analyze the depth of the memory of quantum memory channels generated by a fixed unitary transformation describing the interaction between the principal system and internal degrees of freedom of the process device. We investigate the simplest case of a qubit memory channel with a two-level memory system. In particular, we explicitly characterize all interactions for which the memory depth is finite. We show that the memory effects are either infinite, or they disappear after at most two uses of the channel. Memory channels of finite depth can be to some extent controlled and manipulated by so-called reset sequences. We show that actions separated by the sequences of inputs of the length of the memory depth are independent and constitute memoryless channels.
Plane wave diffraction by a finite plate with impedance boundary conditions.
Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal
2014-01-01
In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.
Plane wave diffraction by a finite plate with impedance boundary conditions.
Directory of Open Access Journals (Sweden)
Rab Nawaz
Full Text Available In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Quantum decoration transformation for spin models
Energy Technology Data Exchange (ETDEWEB)
Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre, E-mail: ors@dfi.ufla.br
2016-09-15
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.
Quantum decoration transformation for spin models
International Nuclear Information System (INIS)
Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de; Rojas, Onofre
2016-01-01
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.
A Design Method for Graded Insulation of Transformers by Transient Electric Field Intensity Analysis
Yamashita, Hideo; Cingoski, Vlatko; Namera, Akihiro; Nakamae, Eihachiro; Kitamura, Hideo
2000-01-01
In this paper, a calculation method for transient electric field distribution inside a transformer impressed with voltage is proposed: The concentrated electric network for the transformer is constructed by dividing transformer windings into several blocks, and the transient voltage and electric field intensity distributions inside the transformer are calculated by using the axisymmetrical finite element method. Moreover, an animated display of the distributions is realized: The visualization...
Army Maintenance System Transformation
National Research Council Canada - National Science Library
Gilbertson, Frank V
2006-01-01
.... Used in conjunction with pertinent historical data and developed with Army transformation goals in mind, General Systems thinking can provide the framework for guiding maintenance transformation...
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
African Journals Online (AJOL)
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN ... the transverse residual stress in the x-direction (σx) had a maximum value of 375MPa ... the finite element method are in fair agreement with the experimental results.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Structural modeling techniques by finite element method
International Nuclear Information System (INIS)
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
$\\delta$-Expansion at Finite Temperature
Ramos, Rudnei O.
1996-01-01
We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.
Finite temperature instability for compactification
International Nuclear Information System (INIS)
Accetta, F.S.; Kolb, E.W.
1986-03-01
We consider finite temperature effects upon theories with extra dimensions compactified via vacuum stress energy (Casimir) effects. For sufficiently high temperature, a static configuration for the internal space is impossible. At somewhat lower temperatures, there is an instability due to thermal fluctuations of radius of the compact dimensions. For both cases, the Universe can evolve to a de Sitter-like expansion of all dimensions. Stability to late times constrains the initial entropy of the universe. 28 refs., 1 fig., 2 tabs
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Quantum Chromodynamic at finite temperature
International Nuclear Information System (INIS)
Magalhaes, N.S.
1987-01-01
A formal expression to the Gibbs free energy of topological defects of quantum chromodynamics (QCD)by using the semiclassical approach in the context of field theory at finite temperature and in the high temperature limit is determined. This expression is used to calculate the free energy of magnetic monopoles. Applying the obtained results to a method in which the free energy of topological defects of a theory may indicate its different phases, its searched for informations about phases of QCD. (author) [pt
Perturbative QCD at finite temperature
International Nuclear Information System (INIS)
Altherr, T.
1989-03-01
We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks
Spinor pregeometry at finite temperature
International Nuclear Information System (INIS)
Yoshimoto, Seiji.
1985-10-01
We derive the effective action for gravity at finite temperature in spinor pregeometry. The temperature-dependent effective potential for the vierbein which is parametrized as e sub(kμ) = b.diag(1, xi, xi, xi) has the minimum at b = 0 for fixed xi, and behaves as -xi 3 for fixed b. These results indicate that the system of fundamental matters in spinor pregeometry cannot be in equilibrium. (author)
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...
Characterization of finite spaces having dispersion points
International Nuclear Information System (INIS)
Al-Bsoul, A. T
1997-01-01
In this paper we shall characterize the finite spaces having dispersion points. Also, we prove that the dispersion point of a finite space with a dispersion points fixed under all non constant continuous functions which answers the question raised by J. C obb and W. Voxman in 1980 affirmatively for finite space. Some open problems are given. (author). 16 refs
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
Surface Plasmon Wave Adapter Designed with Transformation Optics
DEFF Research Database (Denmark)
Zhang, Jingjing; Xiao, Sanshui; Wubs, Martijn
2011-01-01
On the basis of transformation optics, we propose the design of a surface plasmon wave adapter which confines surface plasmon waves on non-uniform metal surfaces and enables adiabatic mode transformation of surface plasmon polaritons with very short tapers. This adapter can be simply achieved...... with homogeneous anisotropic naturally occurring materials or subwavelength grating-structured dielectric materials. Full wave simulations based on a finite-element method have been performed to validate our proposal....
A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature
International Nuclear Information System (INIS)
Majima, H.; Suzuki, A.
2006-01-01
We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators
Finite-size resonance dielectric cylinder in a rectangular waveguide
International Nuclear Information System (INIS)
Chuprina, V.N.; Khizhnyak, N.A.
1988-01-01
The problem on resonance spread of an electromagnetic wave by a dielectric circular cylinder of finite size in a rectangular waveguide is solved by a numerical-analytical method. The cylinder axes are parallel. The cylinder can be used as a resonance tuning element in accelerating SHF-sections. Problems on cutting off linear algebraic equation systems, to which relations of macroscopic electrodynamics in the integral differential form written for the concrete problem considered here are reduced by analytical transformations, are investigated in the stage of numerical analysis. Theoretical dependences of the insertion of the voltage standing wave coefficient on the generator wave length calculated for different values of problem parameters are constracted
Quantum phase space points for Wigner functions in finite-dimensional spaces
Luis Aina, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.
Quantum phase space points for Wigner functions in finite-dimensional spaces
International Nuclear Information System (INIS)
Luis, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas
Rigid finite element method in analysis of dynamics of offshore structures
Energy Technology Data Exchange (ETDEWEB)
Wittbrodt, Edmund [Gdansk Univ. of Technology (Poland); Szczotka, Marek; Maczynski, Andrzej; Wojciech, Stanislaw [Bielsko-Biala Univ. (Poland)
2013-07-01
This book describes new methods developed for modelling dynamics of machines commonly used in the offshore industry. These methods are based both on the rigid finite element method, used for the description of link deformations, and on homogeneous transformations and joint coordinates, which is applied to the modelling of multibody system dynamics. In this monograph, the bases of the rigid finite element method and homogeneous transformations are introduced. Selected models for modelling dynamics of offshore devices are then verified both by using commercial software, based on the finite element method, as well as by using additional methods. Examples of mathematical models of offshore machines, such as a gantry crane for Blowout-Preventer (BOP) valve block transportation, a pedestal crane with shock absorber, and pipe laying machinery are presented. Selected problems of control in offshore machinery as well as dynamic optimization in device control are also discussed. Additionally, numerical simulations of pipe-laying operations taking active reel drive into account are shown.
Rigid Finite Element Method in Analysis of Dynamics of Offshore Structures
Wittbrodt, Edmund; Maczyński, Andrzej; Wojciech, Stanisław
2013-01-01
This book describes new methods developed for modelling dynamics of machines commonly used in the offshore industry. These methods are based both on the rigid finite element method, used for the description of link deformations, and on homogeneous transformations and joint coordinates, which is applied to the modelling of multibody system dynamics. In this monograph, the bases of the rigid finite element method and homogeneous transformations are introduced. Selected models for modelling dynamics of offshore devices are then verified both by using commercial software, based on the finite element method, as well as by using additional methods. Examples of mathematical models of offshore machines, such as a gantry crane for Blowout-Preventer (BOP) valve block transportation, a pedestal crane with shock absorber, and pipe laying machinery are presented. Selected problems of control in offshore machinery as well as dynamic optimization in device control are also discussed. Additionally, numerical simulations of...
Semigroup methods for evolution equations on networks
Mugnolo, Delio
2014-01-01
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...
An operator semigroup in mathematical genetics
Bobrowski, Adam
2015-01-01
This authored monograph presents a mathematical description of the time evolution of neutral genomic regions in terms of the differential Lyapunov equation. The qualitative behavior of its solutions, with respect to different mutation models and demographic patterns, can be characterized using operator semi group theory. Mutation and drift are two of the main genetic forces, which act on genes of individuals in populations. Their effects are influenced by population dynamics. This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions. The effects of demographic change to the asymptotic of the distribution are also covered. The target audience primarily covers researchers and experts in the field but the book may also be beneficial for graduate students.
Automata and automata mappings of semigroups
Plotkin, Boris; Plotkin, Tatjana
2015-01-01
The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are related to cascade connections of automata of the first type. The introduced automata play a significant role in group theory and, hopefully, in the theory of formal languages.
Negotiated Grammar Transformation
V. Zaytsev (Vadim)
2012-01-01
htmlabstractIn this paper, we study controlled adaptability of metamodel transformations. We consider one of the most rigid metamodel transformation formalisms — automated grammar transformation with operator suites, where a transformation script is built in such a way that it is essentially meant
International Nuclear Information System (INIS)
Kibler, M.; Hage Hassan, M.
1991-04-01
A bibliography on the Hurwitz transformations is given. We deal here, with some details, with two particular Hurwitz transformations, viz, the R 4 → R 3 Kustaanheimo-Stiefel transformation and its R 8 → R 5 compact extension. These transformations are derived in the context of Fock-Bargmann-Schwinger calculus with special emphasis on angular momentum theory
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Improved effective potential by nonlinear canonical transformations
International Nuclear Information System (INIS)
Ritschel, U.
1990-01-01
We generalize the familiar gaussian-effective-potential formalism to a class of non-gaussian trial states. With the help of exact nonlinear canonical transformations, expectation values can be calculated analytically and in closed form. A detailed description of our method, particularly for quadratic and cubic transformations, and of the related renormalization procedure is given. Applications to φ 4 -models in various dimensionalities are treated. We find the expected critical behaviour in two space-time dimensions. In three and four dimensions we observe instabilities which go back the incompleteness of the gaussian-based renormalization. In the appendices it is shown that the quadratic transformation leads to a coherent state in a certain limiting case, and the generalization to systems at finite temperature is performed. (orig.)
A Riemann-Hilbert formulation for the finite temperature Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)
2015-06-03
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.
Neural Network Observer-Based Finite-Time Formation Control of Mobile Robots
Directory of Open Access Journals (Sweden)
Caihong Zhang
2014-01-01
Full Text Available This paper addresses the leader-following formation problem of nonholonomic mobile robots. In the formation, only the pose (i.e., the position and direction angle of the leader robot can be obtained by the follower. First, the leader-following formation is transformed into special trajectory tracking. And then, a neural network (NN finite-time observer of the follower robot is designed to estimate the dynamics of the leader robot. Finally, finite-time formation control laws are developed for the follower robot to track the leader robot in the desired separation and bearing in finite time. The effectiveness of the proposed NN finite-time observer and the formation control laws are illustrated by both qualitative analysis and simulation results.
Heat transfer model and finite element formulation for simulation of selective laser melting
Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.
2017-10-01
A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.
Gauge theory for finite-dimensional dynamical systems
International Nuclear Information System (INIS)
Gurfil, Pini
2007-01-01
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory
Gauge invariance and the transformation properties of the electromagnetic four-potential
International Nuclear Information System (INIS)
Eriksen, E.
1979-12-01
The problems which arise when Noether's theorem is applied to the Lagrangian of the electromagnetic theory are investigated. They are shown to be related to the gauge dependence of the standard transformation properties of the potential A(subμ). An alternative transformation equation, which in a certain sense is gauge independent, is introduced for infinitesimal space-time transformations. This transformation leads, by Noether's theorem, directly to the continuity equations for the symmetric energy-momentum tensor and the gauge independent angular momentum tensor. The consequences of the transformation formula for finite space-time transformations are discussed. (Auth.)
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
A transformation of SDL specifications : a step towards the verification
Ioustinova, N.; Sidorova, N.; Bjorner, D.; Broy, M.; Zamulin, A.
2001-01-01
Industrial-size specifications/models (whose state space is often infinite) can not be model checked in a direct way— a verification model of a system is model checked instead. Program transformation is a way to build a finite-state verification model that can be submitted to a model checker.
Transformations Based on Continuous Piecewise-Affine Velocity Fields
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan
2017-01-01
We propose novel finite-dimensional spaces of well-behaved transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volum...
Functionals of finite Riemann surfaces
Schiffer, Menahem
1954-01-01
This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo
International Nuclear Information System (INIS)
Barbarin, F.; Sorba, P.; Ragoucy, E.
1996-01-01
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≅ so (4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G approx=(2, R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) k is briefly presented. (authors)
Simulating QCD at finite density
de Forcrand, Philippe
2009-01-01
In this review, I recall the nature and the inevitability of the "sign problem" which plagues attempts to simulate lattice QCD at finite baryon density. I present the main approaches used to circumvent the sign problem at small chemical potential. I sketch how one can predict analytically the severity of the sign problem, as well as the numerically accessible range of baryon densities. I review progress towards the determination of the pseudo-critical temperature T_c(mu), and towards the identification of a possible QCD critical point. Some promising advances with non-standard approaches are reviewed.
Finite temperature approach to confinement
International Nuclear Information System (INIS)
Gave, E.; Jengo, R.; Omero, C.
1980-06-01
The finite temperature treatment of gauge theories, formulated in terms of a gauge invariant variable as in a Polyakov method, is used as a device for obtaining an effective theory where the confinement test takes the form of a correlation function. The formalism is discussed for the abelian CPsup(n-1) model in various dimensionalities and for the pure Yang-Mills theory in the limit of zero temperature. In the latter case a class of vortex like configurations of the effective theory which induce confinement correspond in particular to the instanton solutions. (author)
Linear and Nonlinear Finite Elements.
1983-12-01
Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y , (1-y)’ 1-y’ 2 - y" (6) that change eq. (5) to V) = , [yŖ(1 + y") - Qy
Covariant gauges at finite temperature
Landshoff, Peter V
1992-01-01
A prescription is presented for real-time finite-temperature perturbation theory in covariant gauges, in which only the two physical degrees of freedom of the gauge-field propagator acquire thermal parts. The propagators for the unphysical degrees of freedom of the gauge field, and for the Faddeev-Popov ghost field, are independent of temperature. This prescription is applied to the calculation of the one-loop gluon self-energy and the two-loop interaction pressure, and is found to be simpler to use than the conventional one.
A finite Hankel algorithm for intense optical beam propagation in saturable medium
International Nuclear Information System (INIS)
Bardin, C.; Babuel-Peyrissac, J.P.; Marinier, J.P.; Mattar, F.P.
1985-01-01
Many physical problems, especially light-propagation, that involve the Laplacian operator, are naturally connected with Fourier or Hankel transforms (in case of axial symmetry), which both remove the Laplacian term in the transformed space. Sometimes the analytical calculation can be handled at its end, giving a series or an integral representation of the solution. Otherwise, an analytical pre-treatment of the original equation may be done, leading to numerical computation techniques as opposed to self-adaptive stretching and rezoning techniques, which do not use Fourier or Hankel transforms. The authors present here some basic mathematical properties of infinite and finite Hankel transform, their connection with physics and their adaptation to numerical calculation. The finite Hankel transform is well-suited to numerical computation, because it deals with a finite interval, and the precision of the calculation can be easily controlled by the number of zeros of J 0 (x) to be taken. Moreover, they use a special quadrature formula which is well connected to integral conservation laws. The inconvenience of having to sum a series is reduced by the use of vectorized computers, and in the future will be still more reduced with parallel processors. A finite-Hankel code has been performed on CRAY-XMP in order to solve the propagation of a CW optical beam in a saturable absorber. For large diffractions or when a very small radial grid is required for the description of the optical field, this FHT algorithm has been found to perform better than a direct finite-difference code
Transforming the Way We Teach Function Transformations
Faulkenberry, Eileen Durand; Faulkenberry, Thomas J.
2010-01-01
In this article, the authors discuss "function," a well-defined rule that relates inputs to outputs. They have found that by using the input-output definition of "function," they can examine transformations of functions simply by looking at changes to input or output and the respective changes to the graph. Applying transformations to the input…
Fidelity estimation between two finite ensembles of unknown pure equatorial qubit states
Energy Technology Data Exchange (ETDEWEB)
Siomau, Michael, E-mail: siomau@physi.uni-heidelberg.de [Physikalisches Institut, Heidelberg Universitaet, D-69120 Heidelberg (Germany); Department of Theoretical Physics, Belarussian State University, 220030 Minsk (Belarus)
2011-09-05
Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation. -- Highlights: → We search for the best strategy for the fidelity estimation. → A measurement-based, a cloning-based and a unified strategies are considered. → The last strategy includes a specific unitary transformation and state estimation. → The unified strategy is shown to be the best among the three.
Biset functors for finite groups
Bouc, Serge
2010-01-01
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
Phase transitions in finite systems
Energy Technology Data Exchange (ETDEWEB)
Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), DSM-CEA / IN2P3-CNRS, 14 - Caen (France); Gulminelli, F. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire
2002-07-01
In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)
Supersymmetry breaking at finite temperature
International Nuclear Information System (INIS)
Kratzert, K.
2002-11-01
The mechanism of supersymmetry breaking at finite temperature is still only partly understood. Though it has been proven that temperature always breaks supersymmetry, the spontaneous nature of this breaking remains unclear, in particular the role of the Goldstone fermion. The aim of this work is to unify two existing approaches to the subject. From a hydrodynamic point of view, it has been argued under very general assumptions that in any supersymmetric quantum field theory at finite temperature there should exist a massless fermionic collective excitation, named phonino because of the analogy to the phonon. In the framework of a self-consistent resummed perturbation theory, it is shown for the example of the Wess-Zumino model that this mode fits very well into the quantum field theoretical framework pursued by earlier works. Interpreted as a bound state of boson and fermion, it contributes to the supersymmetric Ward-Takahashi identities in a way showing that supersymmetry is indeed broken spontaneously with the phonino playing the role of the Goldstone fermion. The second part of the work addresses the case of supersymmetric quantum electrodynamics. It is shown that also here the phonino exists and must be interpreted as the Goldstone mode. This knowledge allows a generalization to a wider class of models. (orig.)
Finite groups and quantum physics
International Nuclear Information System (INIS)
Kornyak, V. V.
2013-01-01
Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.
Phase transitions in finite systems
International Nuclear Information System (INIS)
Chomaz, Ph.; Gulminelli, F.
2002-01-01
In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)
Modeling of NiTiHf using finite difference method
Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad
2018-03-01
NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.
Three dimensional canonical transformations
International Nuclear Information System (INIS)
Tegmen, A.
2010-01-01
A generic construction of canonical transformations is given in three-dimensional phase spaces on which Nambu bracket is imposed. First, the canonical transformations are defined as based on cannonade transformations. Second, it is shown that determination of the generating functions and the transformation itself for given generating function is possible by solving correspondent Pfaffian differential equations. Generating functions of type are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed as the complementary subject. Finally, it is shown that decomposition of canonical transformations is also possible in three-dimensional phase spaces as in the usual two-dimensional ones.
Simulation of Structural Transformations in Heating of Alloy Steel
Kurkin, A. S.; Makarov, E. L.; Kurkin, A. B.; Rubtsov, D. E.; Rubtsov, M. E.
2017-07-01
Amathematical model for computer simulation of structural transformations in an alloy steel under the conditions of the thermal cycle of multipass welding is presented. The austenitic transformation under the heating and the processes of decomposition of bainite and martensite under repeated heating are considered. Amethod for determining the necessary temperature-time parameters of the model from the chemical composition of the steel is described. Published data are processed and the results used to derive regression models of the temperature ranges and parameters of transformation kinetics of alloy steels. The method developed is used in computer simulation of the process of multipass welding of pipes by the finite-element method.
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Characterization of resonances using finite size effects
International Nuclear Information System (INIS)
Pozsgay, B.; Takacs, G.
2006-01-01
We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra
Finite size scaling and lattice gauge theory
International Nuclear Information System (INIS)
Berg, B.A.
1986-01-01
Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs
Finite element application to global reactor analysis
International Nuclear Information System (INIS)
Schmidt, F.A.R.
1981-01-01
The Finite Element Method is described as a Coarse Mesh Method with general basis and trial functions. Various consequences concerning programming and application of Finite Element Methods in reactor physics are drawn. One of the conclusions is that the Finite Element Method is a valuable tool in solving global reactor analysis problems. However, problems which can be described by rectangular boxes still can be solved with special coarse mesh programs more efficiently. (orig.) [de
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Deciding Full Branching Time Logic by Program Transformation
Pettorossi, Alberto; Proietti, Maurizio; Senni, Valerio
We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-programs.
Laplace Transforms without Integration
Robertson, Robert L.
2017-01-01
Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Chemical Transformation Simulator
The Chemical Transformation Simulator (CTS) is a web-based, high-throughput screening tool that automates the calculation and collection of physicochemical properties for an organic chemical of interest and its predicted products resulting from transformations in environmental sy...
Diffusionless phase transformations
International Nuclear Information System (INIS)
Vejman, K.M.
1987-01-01
Diffusionless phase transformations in metals and alloys in the process of which atomic displacements occur at the distances lower than interatomic ones and relative correspondence of neighbour atoms is preserved, are considered. Special attention is paid to the mechanism of martensitic transformations. Phenomenologic crystallographical theory of martensitic transformations are presented. Two types of martensitic transformations different from the energy viewpoint are pointed out - thermoelastic and non-thermoelastic ones - which are characterized by transformation hysteresis and ways of martensite - initial phase reverse transformation realization. Mechanical effect in the martensitic transformations have been analyzed. The problem of diffusionless formation of ω-phases and the effect of impurities and vacancies on the process are briefly discussed. The role of charge density waves in phase transformations of the second type (transition of initial phase into noncommensurate one) and of the first type (transition of noncommensurate phase into commensurate one) is considered
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Entropy of Baker's Transformation
Institute of Scientific and Technical Information of China (English)
栾长福
2003-01-01
Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.
A first course in finite elements
Fish, Jacob
2007-01-01
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts
Features of finite quantum field theories
International Nuclear Information System (INIS)
Boehm, M.; Denner, A.
1987-01-01
We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)
Burnside structures of finite subgroups
International Nuclear Information System (INIS)
Lysenok, I G
2007-01-01
We establish conditions guaranteeing that a group B possesses the following property: there is a number l such that if elements w, x -1 wx,...,x -l+1 wx l-1 of B generate a finite subgroup G then x lies in the normalizer of G. These conditions are of a quite special form. They hold for groups with relations of the form x n =1 which appear as approximating groups for the free Burnside groups B(m,n) of sufficiently large even exponent n. We extract an algebraic assertion which plays an important role in all known approaches to substantial results on the groups B(m,n) of large even exponent, in particular, to proving their infiniteness. The main theorem asserts that when n is divisible by 16, B has the above property with l=6
Learning Extended Finite State Machines
Cassel, Sofia; Howar, Falk; Jonsson, Bengt; Steffen, Bernhard
2014-01-01
We present an active learning algorithm for inferring extended finite state machines (EFSM)s, combining data flow and control behavior. Key to our learning technique is a novel learning model based on so-called tree queries. The learning algorithm uses the tree queries to infer symbolic data constraints on parameters, e.g., sequence numbers, time stamps, identifiers, or even simple arithmetic. We describe sufficient conditions for the properties that the symbolic constraints provided by a tree query in general must have to be usable in our learning model. We have evaluated our algorithm in a black-box scenario, where tree queries are realized through (black-box) testing. Our case studies include connection establishment in TCP and a priority queue from the Java Class Library.
Yu, Y T; Tuan, P H; Chang, K C; Hsieh, Y H; Huang, K F; Chen, Y F
2016-01-11
Broad-area vertical-cavity surface-emitting lasers (VCSELs) with different cavity sizes are experimentally exploited to manifest the influence of the finite confinement strength on the path-length distribution of quantum billiards. The subthreshold emission spectra of VCSELs are measured to obtain the path-length distributions by using the Fourier transform. It is verified that the number of the resonant peaks in the path-length distribution decreases with decreasing the confinement strength. Theoretical analyses for finite-potential quantum billiards are numerically performed to confirm that the mesoscopic phenomena of quantum billiards with finite confinement strength can be analogously revealed by using broad-area VCSELs.
International Nuclear Information System (INIS)
Sanborn, Graham G.; Shabana, Ahmed A.
2009-01-01
For almost a decade, the finite element absolute nodal coordinate formulation (ANCF) has been used for both geometry and finite element representations. Because of the ANCF isoparametric property in the cases of beams, plates and shells, ANCF finite elements lend themselves easily to the geometric description of curves and surfaces, as demonstrated in the literature. The ANCF finite elements, therefore, are ideal for what is called isogeometric analysis that aims at the integration ofcomputer aided designandanalysis (ICADA), which involves the integration of what is now split into the separate fields of computer aided design (CAD) and computer aided analysis (CAA). The purpose of this investigation is to establish the relationship between the B-spline and NURBS, which are widely used in the geometric modeling, and the ANCF finite elements. It is shown in this study that by using the ANCF finite elements, one can in a straightforward manner obtain the control point representation required for the Bezier, B-spline and NURBS geometry. To this end, a coordinate transformation is used to write the ANCF gradient vectors in terms of control points. Unifying the CAD and CAA will require the use of such coordinate transformations and their inverses in order to transform control points to position vector gradients which are required for the formulation of the element transformations in the case of discontinuities as well as the formulation of the strain measures and the stress forces based on general continuum mechanics theory. In particular, fully parameterized ANCF finite elements can be very powerful in describing curve, surface, and volume geometry, and they can be effectively used to describe discontinuities while maintaining the many ANCF desirable features that include a constant mass matrix, zero Coriolis and centrifugal forces, no restriction on the amount of rotation or deformation within the finite element, ability for straightforward implementation of general
Energy Technology Data Exchange (ETDEWEB)
Dudek, K; Glowacki, M; Pietrzyk, M [Akademia Gorniczo-Hutnicza, Cracow (Poland)
1999-07-01
Numerical model describing stresses arising during phase transformations in steels products is presented. The full model consists of three components. The first component uses finite element solution of Fourier equation for an evaluation of the temperature field inside the sample. The second component predicts kinetics of phase transformation occurring during cooling of steel products. Coupling of these two components allows prediction of structure and properties of final products at room temperature. The third component uses elastic-plastic finite element model for prediction of stresses caused by non-uniform temperatures and by changes of volume during transformations. Typical results of simulations performed for cooling of rails after hot rolling are presented. (author)
International Nuclear Information System (INIS)
Sugano, Yoshihiro; Nakanishi, Takanori.
1980-01-01
The materials macroscopically regarded as anisotropic materials such as fiber-reinforced composite materials have become to be used for the structural elements at elevated temperature, and the studies on the problem of thermal stress in anisotropic bodies are carried out actively. The unsteady thermal stress in anisotropic finite circular cylinders has not been analyzed so far. In this study, the problem of unsteady thermal stress in an anisotropic finite circular cylinder having arbitrary surface heat generation in axial direction on the internal and external surfaces, and emitting heat from both ends and the internal and external surfaces, was analyzed. For the analysis of temperature distribution, generalized finite Fourier transformation and finite Hankel transformation were used, and thermal stress and thermal displacement were analyzed by the use of the stress function of Singh. By adopting the function used for the transformation nucleus in generalized finite Fourier transformation as the stress function, the analysis was made without separating symmetric and opposite symmetric problems. Numerical calculation was carried out on the basis of the analytical results, and the effects of the anisotropy in thermal conductivity, Young's modulus and linear expansion on unsteady temperature distribution, thermal stress and thermal displacement were quantitatively examined. (Kako, I.)
Finite-time braiding exponents
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.
Electrostatic shielding of transformers
Energy Technology Data Exchange (ETDEWEB)
De Leon, Francisco
2017-11-28
Toroidal transformers are currently used only in low-voltage applications. There is no published experience for toroidal transformer design at distribution-level voltages. Toroidal transformers are provided with electrostatic shielding to make possible high voltage applications and withstand the impulse test.
Defense Business Transformation
2009-12-01
Defense Business Transformation by Jacques S. Gansler and William Lucyshyn The Center for Technology and National...REPORT TYPE 3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Defense Business Transformation 5a. CONTRACT NUMBER 5b. GRANT NUMBER...vii Part One: DoD Business Transformation
Transforming the Force and Logistics Transformation
National Research Council Canada - National Science Library
Cook, Katherine M
2006-01-01
U.S. Army transformation strategy addresses the imperative to change the Army from a Cold War-oriented design to one that is more responsive, agile, and adaptable to present and emerging threats across...
Experimental analysis and simulation calculation of the inductances of loosely coupled transformer
Kerui, Chen; Yang, Han; Yan, Zhang; Nannan, Gao; Ying, Pei; Hongbo, Li; Pei, Li; Liangfeng, Guo
2017-11-01
The experimental design of iron-core wireless power transmission system is designed, and an experimental model of loosely coupled transformer is built. Measuring the air gap on both sides of the transformer 15mm inductor under the parameters. The feasibility and feasibility of using the finite element method to calculate the coil inductance parameters of the loosely coupled transformer are analyzed. The system was modeled by ANSYS, and the magnetic field was calculated by finite element method, and the inductance parameters were calculated. The finite element method is used to calculate the inductive parameters of the loosely coupled transformer, and the basis for the accurate compensation of the capacitance of the wireless power transmission system is established.
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.
2017-01-01
. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...
A fast finite-difference algorithm for topology optimization of permanent magnets
Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter
2017-09-01
We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.
International Nuclear Information System (INIS)
Frater, J.; Lestingi, J.; Padovan, J.
1977-01-01
This paper describes the development of an improved semi-analytical finite element for the stress analysis of anisotropic axisymmetric solids subjected to nonsymmetric loads. Orthogonal functions in the form of finite Fourier exponential transforms, which satisfy the equations of equilibrium of the theory of elasticity for an anisotropic solid of revolution, are used to expand the imposed loadings and displacement field. It is found that the orthogonality conditions for the assumed solution reduce the theta-dependency, thus reducing the three dimensional problem to an infinite series of two dimensional problems. (Auth.)
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
International Nuclear Information System (INIS)
Chen, G.Q.; Gao, Z.; Yang, Z.F.
1993-01-01
A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic
Inversion algorithms for the spherical Radon and cosine transform
International Nuclear Information System (INIS)
Louis, A K; Riplinger, M; Spiess, M; Spodarev, E
2011-01-01
We consider two integral transforms which are frequently used in integral geometry and related fields, namely the spherical Radon and cosine transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulae or algorithms for atomic measures have been derived, which are not so important for applications. We focus on two- and three-dimensional cases, where we also show that our method leads to a regularization. Numerical results are presented and show the validity of the resulting algorithms. First, we use synthetic data for the inversion of the Radon transform. Then we apply the algorithm for the inversion of the cosine transform to reconstruct the directional distribution of line processes from finitely many intersections of their lines with test lines (2D) or planes (3D), respectively. Finally we apply our method to analyse a series of microscopic two- and three-dimensional images of a fibre system
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Transformer supply of inductive and resistive loads of a magnetocumulative generator
International Nuclear Information System (INIS)
Kravchenko, A.S.; Lyudaev, R.Z.; Pavlovskij, A.I.; Plyashkevich, L.N.; Shuvalov, A.M.
1981-01-01
Variants of transformer energy outlet from magnetocumulative generator (MCG) to inductive and resistive loads are considered. For engineer calculations of transformer MCG electrotechnical model supplemented with a known from the experiment fact of existence of optimum by energy generator finite inductivity turns to be useful. The possibility of current front shortening in the load using a transformer idle running and current pulse shaping at current damping upon the finishing of generator performance is considered [ru
Highly-Expressive Spaces of Well-Behaved Transformations: Keeping It Simple
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan
We propose novel finite-dimensional spaces of Rn → Rn transformations, n ∈ {1, 2, 3}, derived from (continuously-defined) parametric stationary velocity fields. Particularly, we obtain these transformations, which are diffeomorphisms, by fast and highly-accurate integration of continuous piecewise...... transformations). Its applications include, but are not limited to: unconstrained optimization over monotonic functions; modeling cumulative distribution functions or histograms; time warping; image registration; landmark-based warping; real-time diffeomorphic image editing....
Nonsynchronous Noncommensurate Impedance Transformers
DEFF Research Database (Denmark)
Zhurbenko, Vitaliy; Kim, K
2012-01-01
Nonsynchronous noncommensurate impedance transformers consist of a combination of two types of transmission lines: transmission lines with a characteristic impedance equal to the impedance of the source, and transmission lines with a characteristic impedance equal to the load. The practical...... advantage of such transformers is that they can be constructed using sections of transmission lines with a limited variety of characteristic impedances. These transformers also provide comparatively compact size in applications where a wide transformation ratio is required. This paper presents the data...... matrix approach and experimentally verified by synthesizing a 12-section nonsynchronous noncommensurate impedance transformer. The measured characteristics of the transformer are compared to the characteristics of a conventional tapered line transformer....
Fast downscaled inverses for images compressed with M-channel lapped transforms.
de Queiroz, R L; Eschbach, R
1997-01-01
Compressed images may be decompressed and displayed or printed using different devices at different resolutions. Full decompression and rescaling in space domain is a very expensive method. We studied downscaled inverses where the image is decompressed partially, and a reduced inverse transform is used to recover the image. In this fashion, fewer transform coefficients are used and the synthesis process is simplified. We studied the design of fast inverses, for a given forward transform. General solutions are presented for M-channel finite impulse response (FIR) filterbanks, of which block and lapped transforms are a subset. Designs of faster inverses are presented for popular block and lapped transforms.
Interpretability degrees of finitely axiomatized sequential theories
Visser, Albert
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory-like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB-have suprema. This partially answers a question posed
Interpretability Degrees of Finitely Axiomatized Sequential Theories
Visser, Albert
2012-01-01
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory —like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB— have suprema. This partially answers a question
Finite Topological Spaces as a Pedagogical Tool
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Lectures on zeta functions over finite fields
Wan, Daqing
2007-01-01
These are the notes from the summer school in G\\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Finite p′-nilpotent groups. II
Directory of Open Access Journals (Sweden)
S. Srinivasan
1987-01-01
Full Text Available In this paper we continue the study of finite p′-nilpotent groups that was started in the first part of this paper. Here we give a complete characterization of all finite groups that are not p′-nilpotent but all of whose proper subgroups are p′-nilpotent.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Regularization of finite temperature string theories
International Nuclear Information System (INIS)
Leblanc, Y.; Knecht, M.; Wallet, J.C.
1990-01-01
The tachyonic divergences occurring in the free energy of various string theories at finite temperature are eliminated through the use of regularization schemes and analytic continuations. For closed strings, we obtain finite expressions which, however, develop an imaginary part above the Hagedorn temperature, whereas open string theories are still plagued with dilatonic divergences. (orig.)
∗-supplemented subgroups of finite groups
Indian Academy of Sciences (India)
A subgroup H of a group G is said to be M∗-supplemented in G if ... normal subgroups and determined the structure of finite groups by using some ...... [12] Monakhov V S and Shnyparkov A V, On the p-supersolubility of a finite group with a.
Dynamic pricing and learning with finite inventories
den Boer, A.V.; Zwart, Bert
2013-01-01
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season, perishes. The goal of the seller is to determine a pricing strategy
Dynamic pricing and learning with finite inventories
den Boer, A.V.; Zwart, Bert
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy
Dynamic Pricing and Learning with Finite Inventories
A.P. Zwart (Bert); A.V. den Boer (Arnoud)
2015-01-01
htmlabstractWe study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a
Dynamic pricing and learning with finite inventories
Boer, den A.V.; Zwart, B.
2015-01-01
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy
A Finite Model Property for Intersection Types
Directory of Open Access Journals (Sweden)
Rick Statman
2015-03-01
Full Text Available We show that the relational theory of intersection types known as BCD has the finite model property; that is, BCD is complete for its finite models. Our proof uses rewriting techniques which have as an immediate by-product the polynomial time decidability of the preorder <= (although this also follows from the so called beta soundness of BCD.
Why do probabilistic finite element analysis ?
Thacker, Ben H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
The finite-dimensional Freeman thesis.
Rudolph, Lee
2008-06-01
I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.
Factoring polynomials over arbitrary finite fields
Lange, T.; Winterhof, A.
2000-01-01
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Stochastic delocalization of finite populations
International Nuclear Information System (INIS)
Geyrhofer, Lukas; Hallatschek, Oskar
2013-01-01
The localization of populations of replicating bacteria, viruses or autocatalytic chemicals arises in various contexts, such as ecology, evolution, medicine or chemistry. Several deterministic mathematical models have been used to characterize the conditions under which localized states can form, and how they break down due to convective driving forces. It has been repeatedly found that populations remain localized unless the bias exceeds a critical threshold value, and that close to the transition the population is characterized by a diverging length scale. These results, however, have been obtained upon ignoring number fluctuations (‘genetic drift’), which are inevitable given the discreteness of the replicating entities. Here, we study the localization/delocalization of a finite population in the presence of genetic drift. The population is modeled by a linear chain of subpopulations, or demes, which exchange migrants at a constant rate. Individuals in one particular deme, called ‘oasis’, receive a growth rate benefit, and the total population is regulated to have constant size N. In this ecological setting, we find that any finite population delocalizes on sufficiently long time scales. Depending on parameters, however, populations may remain localized for a very long time. The typical waiting time to delocalization increases exponentially with both population size and distance to the critical wind speed of the deterministic approximation. We augment these simulation results by a mathematical analysis that treats the reproduction and migration of individuals as branching random walks subject to global constraints. For a particular constraint, different from a fixed population size constraint, this model yields a solvable first moment equation. We find that this solvable model approximates very well the fixed population size model for large populations, but starts to deviate as population sizes are small. Nevertheless, the qualitative behavior of the
An introduction to finite tight frames
Waldron, Shayne F D
2018-01-01
This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Key features and topics: * First book entirely devoted to finite frames * Extensive exercises and MATLAB examples for classroom use * Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames * Later chapters delve into general theory details and recent research results * Many illustrations showing the special aspects of the geometry of finite frames * Provides an overview of the field of finite tight frames * Discusses future research directions in the field Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook ...
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
Finite density aspects of leptogenesis
International Nuclear Information System (INIS)
Hohenegger, Andreas
2010-01-01
Leptogenesis takes place in the early universe at high temperatures and densities and a deviation from equilibrium in the decay of heavy Majorana neutrinos is a fundamental requirement for the generation of the asymmetry. The equations, commonly used for its description, are largely based on classical Boltzmann equations (BEs) while the source of CP-violation is a quantum interference phenomenon. In view of this clash, it is desirable to study such processes in terms of non-equilibrium quantum field theory. On the other hand, it is simpler to solve BEs rather than the corresponding quantum field theoretical ones. Therefore, we derive modified BEs from first principles in the Kadanoff-Baym (KB) formalism. The results, found for a simple toy model, can be applied to popular phenomenological scenarios by analogy. This approach uncovers structural differences of the corrected equations and leads to different results for the form of the finite density contributions to the CP-violating parameter. In the case of degenerate heavy neutrino masses, corresponding to the popular scenario of resonant leptogenesis, it allows to explicitly distinguish between regimes where BEs are applicable or inapplicable.
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Finite approximations in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems
What is finiteness? (Abhishek Banerjee) (Indian Institute of Science)
Indian Academy of Sciences (India)
Do finites get enough respect? • Finiteness is easy, no? • Just count whether 1, 2, 3,... • But then we miss out on the true richness of the concept of finitness. • There's more finiteness around. In fact, finiteness is what helps us really understand things. 5 ...
Transformative environmental governance
Chaffin, Brian C.; Garmestani, Ahjond S.; Gunderson, Lance H.; Harm Benson, Melinda; Angeler, David G.; Arnold, Craig Anthony (Tony); Cosens, Barbara; Kundis Craig, Robin; Ruhl, J.B.; Allen, Craig R.
2016-01-01
Transformative governance is an approach to environmental governance that has the capacity to respond to, manage, and trigger regime shifts in coupled social-ecological systems (SESs) at multiple scales. The goal of transformative governance is to actively shift degraded SESs to alternative, more desirable, or more functional regimes by altering the structures and processes that define the system. Transformative governance is rooted in ecological theories to explain cross-scale dynamics in complex systems, as well as social theories of change, innovation, and technological transformation. Similar to adaptive governance, transformative governance involves a broad set of governance components, but requires additional capacity to foster new social-ecological regimes including increased risk tolerance, significant systemic investment, and restructured economies and power relations. Transformative governance has the potential to actively respond to regime shifts triggered by climate change, and thus future research should focus on identifying system drivers and leading indicators associated with social-ecological thresholds.
Quantized Bogoliubov transformations
International Nuclear Information System (INIS)
Geyer, H.B.
1984-01-01
The boson mapping of single fermion operators in a situation dominated by the pairing force gives rise to a transformation that can be considered a quantized version of the Bogoliubov transformation. This transformation can also be obtained as an exact special case of operators constructed from an approximate treatment of particle number projection, suggesting a method of obtaining the boson mapping in cases more complicated than that of pairing force domination
Clifford algebra in finite quantum field theories
International Nuclear Information System (INIS)
Moser, M.
1997-12-01
We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)
Phase transformation and diffusion
Kale, G B; Dey, G K
2008-01-01
Given that the basic purpose of all research in materials science and technology is to tailor the properties of materials to suit specific applications, phase transformations are the natural key to the fine-tuning of the structural, mechanical and corrosion properties. A basic understanding of the kinetics and mechanisms of phase transformation is therefore of vital importance. Apart from a few cases involving crystallographic martensitic transformations, all phase transformations are mediated by diffusion. Thus, proper control and understanding of the process of diffusion during nucleation, g
Coaxial pulse matching transformer
International Nuclear Information System (INIS)
Ledenev, V.V.; Khimenko, L.T.
1986-01-01
This paper describes a coaxial pulse matching transformer with comparatively simple design, increased mechanical strength, and low stray inductance. The transformer design makes it easy to change the turns ratio. The circuit of the device and an expression for the current multiplication factor are presented; experiments confirm the efficiency of the transformer. Apparatus with a coaxial transformer for producing high-power pulsed magnetic fields is designed (current pulses of 1-10 MA into a load and a natural frequency of 100 kHz)
Distributed photovoltaic grid transformers
Shertukde, Hemchandra Madhusudan
2014-01-01
The demand for alternative energy sources fuels the need for electric power and controls engineers to possess a practical understanding of transformers suitable for solar energy. Meeting that need, Distributed Photovoltaic Grid Transformers begins by explaining the basic theory behind transformers in the solar power arena, and then progresses to describe the development, manufacture, and sale of distributed photovoltaic (PV) grid transformers, which help boost the electric DC voltage (generally at 30 volts) harnessed by a PV panel to a higher level (generally at 115 volts or higher) once it is
Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam
Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa
2017-08-01
In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.
International Nuclear Information System (INIS)
Steudel, H.
1980-01-01
It is shown that the two-parameter manifold of Baecklund transformations known for the nonlinear Schroedinger equation can be generated from one Baecklund transformation with specified parameters by use of scale transformation and Galilean transformation. (orig.)
The Fourier transform of tubular densities
Prior, C B
2012-05-18
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
The Fourier transform of tubular densities
International Nuclear Information System (INIS)
Prior, C B; Goriely, A
2012-01-01
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)
An outgoing energy flux boundary condition for finite difference ICRP antenna models
International Nuclear Information System (INIS)
Batchelor, D.B.; Carter, M.D.
1992-11-01
For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods
Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch