
Whiteness formula in CIELAB uniform color space
Guoxin He; Mingxun Zhou
20070101
@@ Many attempts have been made to standardize the calculation of whiteness. Whiteness formulas currently in use satisfactorily characterize the appearance of commercial whiteness. However, they have poor correlations with the observers' evaluations, and are often unsuccessful in assessing tinted white samples.A whiteness formula in the CIELAB uniform color space is developed in this paper. Several whiteness formulas are analyzed and compared. The experimental results show that the whiteness formula in the CIELAB uniform color space agrees well with the visual ranking, and it is superior to the CIE whiteness formula and the others in visual correlativity, uniformity and applicability.

Cottingham formula and nucleon polarisabilities
The difference between the electromagnetic selfenergies of proton and neutron can be calculated with the Cottingham formula, which expresses the selfenergies as an integral over the electroproduction cross sections  provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameterfree sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment. (orig.)

Multidimensional Datawarehouse with Combination Formula
Warnars, Spits
20100101
Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional datawarehouse is incomplete. Multidimensional give ability to analyze business measurement in many different ways. Multidimensional is also synonymous with online analytical processing (OLAP). By using some concepts in datawarehouse like slicedice,drill down and roll up will increase the ability of multidimensional datawarehouse. The research question and the discussing for this paper are how much deepest the multidimensional ability from each fact table in datawarehouse. By using the statistic combination formula we try to explore the combination that can be yielded from each dimension in hypercubes, the entire of dimensi combination, minimum combination and maximum combination.

Cottingham formula and nucleon polarisabilities
Gasser, J.; Leutwyler, H. [Universitaet Bern, Albert Einstein Center for Fundamental Physics, Institut fuer theoretische Physik, Bern (Switzerland); Hoferichter, M. [Universitaet Bern, Albert Einstein Center for Fundamental Physics, Institut fuer theoretische Physik, Bern (Switzerland); Technische Universitaet Darmstadt, Institut fuer Kernphysik, Darmstadt (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany); University of Washington, Institute for Nuclear Theory, Seattle, WA (United States); Rusetsky, A. [Universitaet Bonn, HelmholtzInstitut fuer Strahlen und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Bonn (Germany)
20150815
The difference between the electromagnetic selfenergies of proton and neutron can be calculated with the Cottingham formula, which expresses the selfenergies as an integral over the electroproduction cross sections  provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameterfree sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment. (orig.)

Black hole interior mass formula
We argue by explicit computations that, although the area product, horizon radii product, entropy product, and irreducible mass product of the event horizon and Cauchy horizon are universal, the surface gravity product, the surface temperature product and the Komar energy product of the said horizons do not seem to be universal for KerrNewman black hole spacetimes. We show the black hole mass formula on the Cauchy horizon following the seminal work by Smarr [Phys Rev Lett 30:71 (1973), Phys Rev D 7:289 (1973)] for the outer horizon. We also prescribe the four laws of black hole mechanics for the inner horizon. A new definition of the extremal limit of a black hole is discussed. (orig.)

Cosmological parallaxdistance formula
Singal, Ashok K.
20150901
The standard cosmological parallaxdistance formula, as found in the literature, including textbooks and reference books on cosmology, requires a correction. This correction stems from the fact that in the standard textbook derivation it has been ignored that any chosen baseline in a gravitationally bound system does not partake in the cosmological expansion. Though the correction is available in the literature for some time, the textbooks still continue to use the older, incorrect formula, and its full implications are not yet fully realized. Apart from providing an alternate correct, closedform expression that is more suitable and convenient for computations for certain limiting cases of FRW () world models, we also demonstrate how one can compute parallax distance for the currently favored flatspace acceleratinguniverse (, ) cosmologies. Further, we show that the correction in parallax distance at large redshifts could amount to a factor of three or even more. Moreover, even in an infinite universe the parallax distance does not increase indefinitely with redshift and that even the farthest possible observable point may have a finite parallax angle, a factor that needs to be carefully taken into account when using distant objects as the background field against which the parallax of a foreground object is to be measured. Some other complications that could arise in parallax measurements of a distant source, like that due to the deflection of incoming light by the gravitation field of the Sun and other planetary bodies in the solar system, are pointed out.

Welfare Effects of Tariff Reduction Formulas
Guldager, Jan G.; Schröder, Philipp J.H.
WTO negotiations rely on tariff reduction formulas. It has been argued that formula approaches are of increasing importance in trade talks, because of the large number of countries involved, the wider dispersion in initial tariffs (e.g. tariff peaks) and gaps between bound and applied tariff rates....... This paper presents a two country intraindustry trade model with heterogeneous firms subject to high and low tariffs. We examine the welfare effects of applying three different tariff reduction formulas proposed in the literature i) a proportional cut, ii) the Swiss formula and iii) a compression...... formula. No single formula dominates for all conditions. The ranking of the three tools depends on the degree of product differentiation in the industry, and the achieved reduction in the average tariff....

Mathematical Formula Search using Natural Language Queries
YANG, S.
20141101
Full Text Available This paper presents how to search mathematical formulae written in MathML when given plain words as a query. Since the proposed method allows natural language queries like the traditional Information Retrieval for the mathematical formula search, users do not need to enter any complicated math symbols and to use any formula input tool. For this, formula data is converted into plain texts, and features are extracted from the converted texts. In our experiments, we achieve an outstanding performance, a MRR of 0.659. In addition, we introduce how to utilize formula classification for formula search. By using class information, we finally achieve an improved performance, a MRR of 0.690.

Elements and formulae of special relativity
Guggenheim, E A
20130101
Elements and Formulae of Special Relativity presents elements and formulas of the theory of special relativity and covers topics ranging from kinematics and propagation of light to mechanics of single bodies, hydrodynamics, and thermodynamics. Vector operators, electromagnetic fields, electrodynamics, and statistical mechanics are also explored. This book is comprised of 13 chapters and begins by introducing the reader to the kinematics of special relativity, paying particular attention to formulas required for transformations between two frames of reference. Attention then turns to the propag

Developing a Weighted Collection Development Allocation Formula
Bailey, Jeff; Creibaum, Linda
20150101
In this session the presenters demonstrated and discussed how to create a spreadsheet‐based library collection development allocation formula to help acquisitions personnel better manage their library’s limited collection development resources. The presenters demonstrated and led participants through Arkansas State University’s process of creating an Excel‐based formula that utilizes criteria relevant to their specific library and institution. Key to the success of this formula is the use of ...

Rotational Crofton formulae for flagged intrinsic volumes
Auneau, Jeremy Michel
integration is over all sections containing the fixed point origo. Our main result is a local stereological analogue to the wellknown Crofton formula. More precisely, we derive geometric formulae that relate new flagged intrinsic volumes of a set with the flagged intrinsic volumes of its sections, . The...... development of a potential local stereological analogue of the famous principal kinematic formula is also discussed....

A General Framework for Probabilistic Characterizing Formulae
Sack, Joshua; Zhang, Lijun
20120101
Recently, a general framework on characteristic formulae was proposed by Aceto et al. It offers a simple theory that allows one to easily obtain characteristic formulae of many nonprobabilistic behavioral relations. Our paper studies their techniques in a probabilistic setting. We provide a...... general method for determining characteristic formulae of behavioral relations for probabilistic automata using fixedpoint probability logics. We consider such behavioral relations as simulations and bisimulations, probabilistic bisimulations, probabilistic weak simulations, and probabilistic forward...

The fringe capacitance formula of microstructures
This paper presents a fringe capacitance formula of microstructures. The formula is derived by curve fitting on ANSYS simulation results. Compared with the ANSYS and experimental results, the deviation is within ±2%. The application to determine the pullin voltage of an electrostatic microbeam is demonstrated, which agrees very well with the experimental data. The formula presented is very accurate, yields explicit physical meanings and is applicable to common dimension ranges for MEMS devices. (paper)

Column Holdup Formula of Soil Solute Transport
无
20000101
The shortcomings of the present two formulae for describing column holdup are analyzed and deductions are made to find a new formula. The column holdup, Hw, described by the new formula is dimensional,and related to soil solute transport kinesis and column physical properties. Compared with the other two column holdups, Hw is feasible to describe dimensional column holdup during solute transport process. The relationships between Hw and retardation factor, R, in different solute transport boundary conditions are established.

Poincare's relativistic DopplerFizeau formula
Pierseaux, Yves
20060101
We deduce from Poincare's ellipsoidal wavefronts a relativistic DopplerFizeau formula that is not the same as 1905 Einstein's one. Longitudinally, Einstein's formula and Poincare's formula are the same. The question of an experimental test is connected with the possibility or the impossibility of directly measuring the relativistic transverse effect. Hasselkamp's 1978 experiment becomes a crucial experiment because Poincare's relativistic kinematics predicts an expansion of sapce directly co...

NonCommutative QBinomial Formula
Nalci, Sengul; Pashaev, Oktay
20120101
In this paper, we found new qbinomial formula for Qcommutative operators. Expansion coefficients in this formula are given by qbinomial coefficients with two bases (q,Q), determined by Qcommutative qPascal triangle. Our formula generalizes all wellknown binomial formulas in the form of Newton, Gauss, symmetrical, noncommutative and BinetFibonacci binomials. By our noncommutative qbinomial, we introduce qanalogue of function of two noncommutative variables, which could be used in s...

Superfluid Kubo Formulas from Partition Function
Chapman, Shira; Oz, Yaron
20140101
Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stressenergy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are nondissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems.

A rotational integral formula for intrinsic volumes
Jensen, Eva Bjørn Vedel; Rataj, J.
20080101
A rotational version of the famous Crofton formula is derived. The motivation for deriving the formula comes from local stereology, a new branch of stereology based on sections through fixed reference points. The formula shows how rotational averages of intrinsic volumes measured on sections...... passing through fixed points are related to the geometry of the sectioned object. In particular it is shown how certain weighting factors, appearing in the rotational integral formula, can be expressed in terms of hypergeometric functions. Close connections to geometric tomography will be pointed out...

Rotational versions of the Crofton formula
Jensen, Eva B. Vedel
19950101
Inspired by recent developments in stereology, rotational versions of the Crofton formula are derived. The first version involves rotation averages of Minkowski functionals. It is shown that for the special case where the Minkowski functional is surface area, the rotation average can be expressed...... in terms of hypergeometric functions. The second rotational version of the Crofton formula solves the `opposite' problem of finding functions with rotation averages equal to the Minkowski functionals. For the case of surface area, hypergeometric functions appear again. The second type of rotational...... Crofton formula has applications in local stereology. As a byproduct, a formula involving mixed volumes is found....

AN ANALYTICAL REFLECTION OF FORMULAIC LANGUAGE
LiuSiping
20040101
This paper gives a brief panorama of formulaic language, inwhich some of the author's analytical and critical reflections canbe found. First, a rough review is made of various definitionsand identification of formulaic language, a topic that hasremained unsettled to date (Wray, 2000 ). Among thediversified terminology, my own definition is included as areflection of my understating. Next, transferability ofunanalysed formulae to analytical competence, will follow. Asthis topic has aroused heated discussion, it is very hard to reacha consensus. The last section, under the title of rationale andfunctions, is devoted to various features of formulaic language,which include econornicality, acceptability, dependability, anddifficulty.