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This paper refers to Langlands' big set of notes devoted to the question if the (normalized) local Hecke–Tate root number Δ=Δ(E,χ)$\Delta =\Delta (E,\chi)$, where E is a finite separable extension of a fixed nonarchimedean local field F, and χ a quasicharacter of E×$E^\times$, can be appropriately extended to a local ε‐factor εΔ=εΔ(E,ρ)$\varepsilon _\Delta =\varepsilon _\Delta (E,\rho)$ for all virtual representations ρ of the corresponding Weil group WE$W_E$. Whereas Deligne has given a relatively short proof by using the global Artin–Weil L‐functions, the proof of Langlands is purely local and splits into two parts: the algebraic part to find a minimal set of relations for the functions Δ, such that the existence (and unicity) of εΔ$\varepsilon _\Delta$ will follow from these relations; and the more extensive arithmetic part to give a direct proof that all these relations are actually fulfilled. Our aim is to cover the algebraic part of Langlands' notes, which can be done completely in the framework of representations of solvable profinite groups, where two modifications of Brauer's theorem play a prominent role. [ABSTRACT FROM AUTHOR]

In this article, an enhanced arithmetic optimization algorithm (EAOA) is utilized to resolve the optimal reactive power dispatch problem (ORPD) of power plants, which is a non‐linear, non‐smooth, complex optimization problem. Typically, it is formulated as a constrained optimal power flow problem. This paper utilizes the gamma distribution to generate initial random solutions, which improves the accuracy of the arithmetic optimization algorithm (AOA). The original mode of deviation of math optimizer accelerated (MOA) is replaced with the improved pattern of change in the prey's energy in Harris Hawk Optimization (HHO), which creates a superior balance between the exploration and exploitation of AOA. This paper implements logarithmic and exponential operators in place of division and multiplication operators, which improves the exploration ability of AOA and also utilizes the gamma distribution in the generation of random numbers, which are essential for the selection of operators in both search phase which enlarges the search area and improves the global optimum solution. A parametric analysis is performed on 10 benchmark functions for nine possible values before selecting the algorithm's initial parameters. A comparative statistical analysis along with Friedman's test is carried out on 23 benchmark functions to test the overall performance as compared to Sine‐Cosine Algorithm (SCA), Swarm‐Salp Algorithm, Grey Wolf Optimization (GWO), and basic Arithmetic Optimization Algorithm (AOA). EAOA is applied to the IEEE 57 bus system for optimal reactive power control. EAOA reports a significant reduction in a power loss of 23.2 MW, which is 18.596% smaller than the system's base case power loss of 28.5 MW as compared to Artificial Bee Colony (ABC), Firefly Algorithm (FA), Bat‐inspired Algorithm (BAT), Cuckoo Search Algorithm (CSA), and Modified Ant Lion Algorithm (MALO) which reports a reduction in a power loss of 14.73%, 15.43%, 15.43%, 16.14%, and 16.14% respectively. EAOA reduces the TVD to 0.76 pu, compared to ABC, FA, BAT, CSA, and MALO, which minimizes the TVD to 0.84, 0.82, 0.88, 0.82, and 0.79, respectively. This proves that EAOA performs better in resolving ORCP problems regarding the quality of solutions and convergence. A detailed comparative statistical analysis of EAOA with CSA, BAT, and WOA (Whale Optimization Algorithm) is conducted in terms of Probability Distribution Functions (PDF) and Cumulative Distribution Functions (CDF), along with the Wilcoxson sign rank test, which proves that EAOA gives the solution with a higher degree of precision. [ABSTRACT FROM AUTHOR]

There is a close relationship between the embedded topology of complex plane curves and the (group‐theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves that include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper, we consider curve arrangements that contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples, which show the interplay between topology, geometry, and arithmetic. [ABSTRACT FROM AUTHOR]

Some decision‐making problems are required to be analysed using insufficient and vague information under an extended space of fuzziness, considering flexibility in the decision‐making process and the interdependency and interaction between the criteria. To tackle these challenges, a spherical fuzzy set (SFS), which is an extension of the ordinary picture fuzzy set (PFS), can be used to fulfil the requirement of an extended space of fuzziness by quantifying uncertainty. Similarly, the Frank operations can provide flexibility to the decision‐making process due to the involvement of a parameter, whereas the Choquet integral considers all possible interactive characteristics between different criteria. Therefore, this paper integrates these three important concepts to make more sound and realistic decisions by extending the existing arithmetic operation for spherical fuzzy numbers (SFNs) using Frank t‐norm and t‐conorm. In addition, the paper introduces some novel Choquet‐Frank aggregation operators, such as spherical fuzzy Choquet‐Frank averaging (SFCFA) and spherical fuzzy Choquet‐Frank geometric (SFCFG). To demonstrate the effectiveness of the proposed operators, a multi‐criteria decision making (MCDM) problem related to the selection of an enterprise resource planning (ERP) system is analysed for the available five options χ1,χ2,χ3,χ4, and χ5. Sensitivity analysis is performed to investigate the impact of taking variation in parameter values (θ) on aggregated values. Results confirmed that the best alternatives for SFCFA and SFCFG operators are χ3 and χ5, respectively, while χ2 is the worst alternative for both these operators. To show the effectiveness of the proposed operators, a comparative analysis has been performed to compare the results obtained from other existing aggregation operators. Results concluded that the findings resemble most of the existing operators which confirms the feasibility of the proposed operators. [ABSTRACT FROM AUTHOR]

This paper discusses a longitudinal study with children with Apert syndrome aged between 4 and 11 years. There has long been an interest in the role of fingers in the development of early number skills and arithmetic. As children with Apert syndrome are born with complex fusions of their fingers, they have to undergo several surgical procedures in order to obtain individuated fingers. This has implications for their finger mobility and finger awareness. It has been suggested that children with Apert syndrome have specific difficulties with early number and arithmetic activities. The findings from this study suggest that engaging children with Apert syndrome in activities that develop finger awareness (finger gnosis) and finger mobility (fine motor skills) may have a positive impact on their ability to engage with appropriate mathematics curricula at school. This is relevant to all those involved in the care of children with Apert syndrome and will be of particular relevance to those involved in early childhood and primary education. This study also provides new insights into the role of finger use in the development of skills and understanding in early number and arithmetic. [ABSTRACT FROM AUTHOR]

The COVID‐19 crisis has revived an old heated debate on whether significant increases in the money supply ultimately lead to higher inflation. Some observers have alluded to the quantity theory of money for that purpose, though in our view, this has sometimes been in a misleading way. Against this background, this paper seeks to clarify several aspects of the quantity theory of money, which are useful to apply it fairly in the current world. First, we review the meaning of the velocity term in the quantity equation. We argue that it has no relevance as a behavioural concept: there is no such thing as a 'desired velocity'. Rather, income velocity should be seen as a variable deriving from a system of parameters and variables related to money demand, as the monetarist approach clearly puts it, with no intrinsic relevance. Second, we clarify the practical relevance that the quantity theory approach can bear in the 21st century. Third, we review the channels and assumptions underlying the asserted quantity theory link between money growth and inflation. In light of our analysis, we conclude that the high money growth rates seen since the pandemic outbreak are unlikely to translate into higher inflation rates. [ABSTRACT FROM AUTHOR]

The puzzling observation that the famous Euler's formula for three‐dimensional polyhedra V − E + F = 2 or Euler characteristic χ = V − E + F − I = 1 (where V, E, F are the numbers of the bounding vertices, edges and faces, respectively, and I = 1 counts the single solid itself) when applied to space‐filling solids, such as crystallographic asymmetric units or Dirichlet domains, are modified in such a way that they sum up to a value one unit smaller (i.e. to 1 or 0, respectively) is herewith given general validity. The proof provided in this paper for the modified Euler characteristic, χm = Vm − Em + Fm − Im = 0, is divided into two parts. First, it is demonstrated for translational lattices by using a simple argument based on parity groups of integer‐indexed elements of the lattice. Next, Whitehead's theorem, about the invariance of the Euler characteristic, is used to extend the argument from the unit cell to its asymmetric unit components. [ABSTRACT FROM AUTHOR]

In this paper, the general case of normal discrete Hausdorff operators in L2(Rd) is studied. The main result states that under some natural arithmetic condition, the spectrum of such an operator is rotationally invariant. Several special cases and applications are considered. [ABSTRACT FROM AUTHOR]

Wittgenstein's conception of logical and conceptual truth is often thought to rival that of the logical positivists. This paper argues that there are important respects in which these conceptions complement each other. Analyticity, in the positivists' sense, coincides, not with Wittgenstein's notion of a grammatical proposition, but rather with his notion of a tautology. Grammatical propositions can usually be construed as analyticity postulates in Carnap's sense of the term. This account of grammatical and analytic propositions will be illustrated by appeal to logical, conceptual and arithmetic truths. Its consequences for an analysis of corresponding modal notions will be indicated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new explicit series expansion formula for the price of an arithmetic Asian option under the Black–Scholes model and Merton's jump‐diffusion model. The method is based on an equivalence in law relation together with the diffusion operator integral method proposed by Heath and Platen. The method yields explicit series expansion formula for the Asian options' prices. The theoretical convergence of the expansion to the true value is established. We also consider the American Asian option (i.e., Amerasian option) and derive the corresponding expansion formula through the early exercise premium representation. Numerical results illustrate the accuracy and efficiency of the method as compared with benchmarks in the literature. [ABSTRACT FROM AUTHOR]

Summary: The paper introduces the concept of higher order summative cofactors (HOSCs) to the circuit analysis. Although the concept is not new, it is not well known. In the paper, some mathematical background of HOSCs is presented. The further development of the concept of HOSC will yield computer implementation arithmetic of HOSC. A cancellation‐free symbolic analysis technique, which is based on HOSC arithmetic, is presented. This technique allows results to be created directly from a netlist in the form of a binary decision diagram, which is called a parameter decision diagram. Additionally, HOSC arithmetic allows the calculation to be started in many places (sometimes distant) simultaneously. The techniques of rolling up the already analyzed parts of a circuit, which is built into HOSC arithmetic, result in a novel multilevel hierarchical analysis method that is called hierarchical parameter decision diagram (HPDD). Unlike in most hierarchical methods, the results that are obtained based on the subcircuit representation in HPDD always maintain a cancellation‐free form. The HPDD always represents the sum of the product form, which is heavily compressed due to the self‐similarities of the actual circuit. The time that is required for any recalculation of the transfer functions is greatly reduced. Analysis of models that are based on pathological components is also a natural consequence of using HOSC arithmetic. [ABSTRACT FROM AUTHOR]

The Apéry numbers of Fano varieties are asymptotic invariants of their quantum differential equations. In this paper, we initiate a program to exhibit these invariants as (mirror to) limiting extension classes of higher cycles on the associated Landau–Ginzburg (LG) models — and thus, in particular, as periods. We also construct an Apéry motive, whose mixed Hodge structure is shown, as an application of the decomposition theorem, to contain the limiting extension classes in question. Using a new technical result on the inhomogeneous Picard–Fuchs equations satisfied by higher normal functions, we illustrate this proposal with detailed calculations for LG‐models mirror to several Fano threefolds. By describing the "elementary" Apéry numbers in terms of regulators of higher cycles (i.e., algebraic K$K$‐theory/motivic cohomology classes), we obtain a satisfying explanation of their arithmetic properties. Indeed, in each case, the LG‐models are modular families of K3$K3$ surfaces, and the distinction between multiples of ζ(2)$\zeta (2)$ and ζ(3)$\zeta (3)$ (or (2πi)3$(2\pi \mathbf {i})^3$) translates ultimately into one between algebraic K1$K_1$ and K3$K_3$ of the family. [ABSTRACT FROM AUTHOR]

In this paper we provide some applications of the norm form in some quaternion division algebras over rational field, and we give some properties of Fibonacci sequence and Fibonacci sequence in connection to quaternion elements. We provide some properties of the norm of a rational quaternion algebra, in connection to the famous Lagrange's four‐square theorem and its generalizations given by Ramanujan. Moreover, we prove some results regarding the arithmetic of integer quaternions defined on some division quaternion algebras, and we define and give properties of some special quaternions by using Fibonacci sequences. [ABSTRACT FROM AUTHOR]

A negative relationship between mathematics anxiety (MA) and mathematics performance is well documented. One suggested explanation for this relationship is that MA interferes with the cognitive processes needed when solving mathematics problems. A demand for using more cognitive effort (e.g., when performing harder mathematics problems), can be traced as an increase in pupil dilation during the performance. However, we lack knowledge of how MA affects this relationship between the problem difficulty and cognitive effort. This study investigated, for the first time, if MA moderates the effect of arithmetic (i.e., multiplication) problem difficulty on cognitive effort. Thirty‐four university students from Norway completed multiplication tasks, including three difficulty levels of problems, while their cognitive effort was also measured by means of pupil dilation using an eye tracker. Further, the participants reported their MA using a questionnaire, and arithmetic competence, general intelligence, and working memory were measured with paper‐pencil tasks. A linear mixed model analysis showed that the difficulty level of the multiplication problems affected the cognitive effort so that the pupil dilated more with harder multiplication problems. However, we did not find a moderating effect of MA on cognitive effort, when controlling for arithmetic competence, general intelligence, and working memory. This suggests that MA does not contribute to cognitive effort when solving multiplication problems. [ABSTRACT FROM AUTHOR]

Using the symmetric group Sn+1$S_{n+1}$ and related hyperbolic Coxeter groups [3,3,...,3,6]$[3,3,\ldots ,3,6]$, we construct cusped hyperbolic n$n$‐manifolds of small volume having small rank fundamental group, for n⩽5$n\leqslant 5$. In particular, we find a cusped orientable arithmetic hyperbolic 5‐manifold M∗5$M_*^5$ of volume 13ζ(3)/2$13\zeta (3)/2$ with rank(π1(M∗5))=3$\hbox{rank}(\pi _1(M_*^5))=3$, starting from the ideal hyperbolic birectified 5‐simplex described in a recent paper by the second author. [ABSTRACT FROM AUTHOR]

This paper shows that the recent trend of separating macroprudential and monetary policies (M&Ms) into two autonomous institutions is undesirable. A strategic (game of chicken type) conflict is likely to occur, whereby each M&M ignores exuberant credit booms, trying to induce the other institution to tighten conditions. This has been observed, for example, in Sweden and Norway after 2010. We postulate a generalised concept of stochastic leadership and argue that greater rigidities give the prudential authority the upper hand strategically on the central bank. We show how this leads to a second type of unpleasant monetarist arithmetic and costly economic fluctuations. [ABSTRACT FROM AUTHOR]

With the increase of nonlinear loads (such as electric arc furnace, electrified railway, etc.) in power system, the harmonic distortion and unbalance of voltage and current are becoming more and more serious. The energy flow in the system is more complex and variable, and the power factor calculation method is controversial. This paper summarizes the influence factors and calculation methods of power factor for nonsinusoidal and unbalanced systems. The calculation methods of arithmetic power factor, vector power factor and effective power factor are compared first, and then the power factor calculation method recommended by IEEE Std 1459‐2010 and its improvement method under three‐phase balance user, active power calculation and metering error are analyzed, and the recommended calculation methods for different situations are given. Finally, future research perspectives and challenges for power factor calculation are pointed out. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

A new approach has been recently developed to study the arithmetic of hyperelliptic curves y2=f(x)$y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of f$f$. Since its introduction, numerous papers have used this machinery of 'cluster pictures' to compute a plethora of arithmetic invariants associated to these curves. The purpose of this user's guide is to summarise and centralise all of these results in a self‐contained fashion, complemented by an abundance of examples. [ABSTRACT FROM AUTHOR]

Quantum B‐algebras are partially ordered algebras characterizing the residuated structure of a quantale. Examples arise in algebraic logic, non‐commutative arithmetic, and quantum theory. A quantum B‐algebra with trivial partial order is equivalent to a group. The paper introduces a corresponding analogue of quantale modules. It is proved that every quantum B‐module admits an injective envelope which is a quantale module. The injective envelope is constructed explicitly as a completion, a multi‐poset version of the completion of Dedekind and MacNeille. [ABSTRACT FROM AUTHOR]

Math fluency (MF) is the ability to quickly and accurately solve simple math exercises. Proficiency in MF is one of the buildings of arithmetic achievement during school. However, so far only paper and pencil tests have been used to assess MF. In the current study, we present the BGU‐MF (Ben‐Gurion University Math Fluency) test, a new computerized tool for MF. MF was assessed by accuracy rates, response times, and the number of performed exercises. In order to examine its reliability, participants performed the test twice. In order to examine its validity, participants performed manual format of MF from the Woodcock–Johnson battery. Results indicated high reliability and validity of the BGU‐MF test. Performance in the BGU‐MF also predicted abilities in the math matriculation exam and psychometric exam. The advantages of the BGU‐MF computerized tool over the manual tool and further implications of the BGU‐MF are discussed. [ABSTRACT FROM AUTHOR]

The SigmaRho Kalman filter is a new implementation useful for design and application in stressful real‐time environments. This filter has been implemented in a satellite navigation receiver. This paper presents application of results of the new mechanization compared with the original matrix form of the Kalman filter and Bierman‐Thornton UDUT‐factored form. A sample problem from the signal processing area is presented with extreme time variation between samples. This problem, often referred to as software radio, requires estimation of signal phase changes in a repetitive signal (carrier) with additive noise where the digital sampling is at a rate well below the carrier repetition rate. The paper also demonstrates a computationally effective implementation of the SigmaRho filter using integer arithmetic. The implementation is successfully applied at sample rates approaching 100 MHz for a carrier at 1.5 GHz, demonstrating its potential as a signal processing tool for high‐speed commercial applications. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of a Schrödinger system with one boundary damping, which consists of two constant coefficients Schrödinger equations coupled through zero‐order terms. First, we show that when ϱ=1,$$ \varrho =1, $$ the one‐dimensional Schrödinger system is not exponentially stable by the asymptotic expansions of eigenvalues. Then, by the frequency domain approach and the multiplier method, we show that the energy decay rate of the multidimensional Schrödinger system is t−1$$ {t}^{-1} $$ for sufficiently smooth initial data when ϱ=1,$$ \varrho =1, $$|α|$$ \mid \alpha \mid $$ is sufficiently small, and the boundary of domain satisfies suitable geometric assumption. Next, by solving the characteristic equation of unbounded operator, we show that the strong stability of the one‐dimensional Schrödinger system is completely determined by ϱ$$ \varrho $$ and α$$ \alpha $$ and give the necessary and sufficient condition that ϱ$$ \varrho $$ and α$$ \alpha $$ satisfy. Finally, by solving the resolvent equation of unbounded operator and using the frequency domain approach, we show that when ϱ≠1$$ \varrho \ne 1 $$ and |α|$$ \mid \alpha \mid $$ is small enough, the energy of the one‐dimensional Schrödinger system decays polynomially and the decay rate depends on the arithmetic property of ϱ.$$ \varrho. $$ [ABSTRACT FROM AUTHOR]

In response to severe fiscal consolidation policies implemented after the Great Recession and the euro area sovereign debt crisis, many have questioned the effectiveness of fiscal consolidations in reducing the burden of public debt. This paper revisits this fundamental policy debate qualitatively and quantitatively, studying conditions under which primary budget balance changes can successfully reduce government debt‐to‐GDP ratios. We first illustrate these conditions through a partial equilibrium setting. We then investigate the conditions quantitatively using a medium‐scale New Keynesian DSGE model calibrated on periphery countries of the euro area. The analysis highlights the critical role of sovereign spreads in driving the debt‐to‐GDP dynamics following a restrictive primary balance shock. Fiscal consolidations turn out to successfully reduce the debt‐to‐GDP even for fairly low elasticities of spreads to fiscal variables. However, their effectiveness is quantitatively moderate and varies crucially with the initial spread level, with the degree of monetary policy accommodation, and with the responsiveness of market investors to economic fundamentals. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternative overall measure, inspired by the notion of average cross‐efficiency, which summarizes achievements across different descending ordering schemes regarding the relative importance of the considered indicators in the Ng model. The proposed overall measure is equal to the arithmetic average of the maximum partial averages across all possible descending ordering schemes. It can also be obtained using the average (across ordering schemes) of the estimated multipliers. We apply the proposed measure to the ABC inventory classification problem, and we compare our results with those by four information theory based methods that may be used for the same purpose, namely the Shannon entropy, distance‐based, weighted least‐square dissimilarity, and maximizing deviation methods. [ABSTRACT FROM AUTHOR]

The greater arithmetic intensity of high‐order finite element discretizations makes them attractive for implementation on next‐generation hardware, but assembly of high‐order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix‐free application of high‐order operators has received significant attention in the literature in the context of Poisson‐type problems, but preconditioners and solvers for inverting more general operators are not very well‐developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high‐order H1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor‐product basis functions on an unstructured mesh of quadrilaterals. Our approach uses a sparsified H1 solver constructed on a low‐order mesh of the nodal points of the underlying high‐order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two‐dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(pd + 1) floating point operation count and optimal O(pd) memory transfer requirements, outperforming existing Maxwell preconditioners in the high‐order regime. [ABSTRACT FROM AUTHOR]

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators. [ABSTRACT FROM AUTHOR]

While response time and accuracy indicate overall performance, their value in uncovering cognitive processes, underlying learning, is limited. A promising online measure, designed to track decision‐making, is computer mouse tracking, where mouse attraction towards different locations may reflect the consideration of alternative response options. Using a speedy arithmetic multiple‐choice game in an online adaptive learning environment, we examined whether mouse movements could reflect arithmetic difficulties when error rates are low. Results showed that mouse movements towards alternative responses in correctly answered questions mapped onto the frequency of errors made in this online learning system. This mapping was stronger for the younger children, as well as for easy arithmetic problems. On an individual level, users showed more mouse movement towards their previously made response errors than towards other alternative options. This opens the possibility of adapting feedback and instruction on an individual basis through mouse tracking. Lay Description: What is currently known about this topic: In online learning environments, detecting systematic difficulties for students during learning is challenging due to the required high success rate.Previous studies have found that computer mouse tracking offers a window into the cognitive process of considering multiple alternatives before deciding.What is lacking is a validation outside the lab, whether mouse tracking can be a source for detecting systematic difficulties students might have. What the paper adds to this: Mouse tracking was implemented outside the lab in a large‐scale online learning environment for primary school children practicing maths.Novel mouse metrics were developed to measure attraction towards multiple distractors instead of one.Findings show that mouse movements reveal cues to arithmetic difficulties without the need for errors. Implications of the study findings: Mouse tracking is a useful tool to investigate difficulties in the learning process in a motivating practice system.Diagnosing these arithmetic misconceptions for individuals can help to adapt feedback and instruction.The developed mouse method can be used for more daily‐life complex designs with multiple attractors. [ABSTRACT FROM AUTHOR]

In this paper, the detection problem of intermittent multiplicative sensor fault is investigated for stochastic uncertain systems. A robust optimal filter is designed according to the criterion of minimum estimation error covariance. Then, based on this, a residual generator is constructed, and the quantitative effect of the fault on it is discussed in detail. After that we design the evaluation function and detection threshold to achieve intermittent fault detection. Our proposed strategy has a recursive form and only includes simple arithmetic operations, thus it is suitable for real‐time online applications. Finally, a simulation example is given to demonstrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper [ABSTRACT FROM AUTHOR]

In recent paper (‘p-adic coupling of mock modular forms and shadows’, Proc. Natl. Acad. Sci. USA, to appear), Guerzhoy, Kent, and Ono prove a result in the theory of harmonic weak Maass forms on the p-adic coupling of mock modular forms and their shadows. As an application, they construct a sequence of weakly holomorphic modular forms which has a p-adic limit that gives the modular parameterization of the cubic arithmetic–geometric mean (AGM). In this paper, we construct odd weight weakly holomorphic forms with non-trivial character to prove an analogous p-adic limit formula for the modular parameterization of the Gauss quadratic AGM. [ABSTRACT FROM PUBLISHER]

Presents a summary of policy on the use of the International of System (S.I.) units. Rules for writing numbers; S.I. units and their multiples; Multiplication and division of units.

The analytic hierarchy process (AHP), proposed by Saaty in 1971, has already become a common decision technique in the field of decision science. In attempting to deal with group decision problems, a vast amount of literature has adopted geometric means or arithmetic means to aggregate the multiple opinions of group decision makers with AHP. However, geometric means and arithmetic means are usually subject to the influence of extreme values, and make use of only simple average types of manipulation to combine the judgments of decision makers which may not practically capture the group preferences among alternatives. In this paper, two aspects of consideration are probed into the construction of a group AHP decision model, which are ‘preferential differences’ to denote the differences of preferential weights among alternatives for each decision maker, and ‘preferential ranks’ to denote the ranks of the alternatives for each decision maker. A comparative analysis is performed to investigate the effectiveness of the proposed model, and a ‘satisfaction index’ is suggested to indicate the satisfactory level of the final obtained group decision. Finally, a feedback interview is carried out to collect the post-model opinions of decision makers in order to understand their acceptance about the proposed model. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm based on a sequence of three modified Newton procedures to solve the constrained minimization problem. In the literature, numerical integration rules for the tetrahedron are available up to order p=15. We obtain integration rules for the tetrahedron from p=2 to p=20, which are computed using multiprecision arithmetic. For p≤15, our approach provides integration rules that have the same or fewer number of integration points than existing rules; for p=16 to p=20, our rules are new. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, rational, weakly singular and trigonometric test functions over tetrahedra with flat and curved faces. In all tests, improvements in accuracy is realized as p is increased, though in some cases nonmonotonic convergence is observed. [ABSTRACT FROM AUTHOR]

In this paper, a solution to initial value problems for fractional‐order linear commensurate multi‐term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag‐Leffler–type functions and the meta‐trigonometric cosine function by using a numerical‐analytical method. The results of presented numerical experiments show that for high accuracy calculations of these functions, the multi‐precision arithmetic must be applied. The approach for solving of the initial value problems for generalized Basset equation, generalized Bagley‐Torvik equation, and multi‐term fractional equation is demonstrated. [ABSTRACT FROM AUTHOR]

Let Qp∼ be the field of p‐adic numbers in the language of rings. In this paper we consider the theory of Qp∼ expanded by two predicates interpreted by multiplicative subgroups αZ and βZ where α,β∈N are multiplicatively independent. We show that the theory of this structure interprets Peano arithmetic if α and β have positive p‐adic valuation. If either α or β has zero valuation we show that the theory of (Qp∼,αZ,βZ) has the NIP ("negation of the independence property") and therefore does not interpret Peano arithmetic. In that case we also prove that the theory is decidable if and only if the theory of (Qp∼,αZβZ) is decidable. [ABSTRACT FROM AUTHOR]

This paper initiates a research program that seeks to recover algebro‐geometric Galois representations from combinatorial data. We study tropicalizations equipped with symmetries coming from the Galois‐action present on the lattice of 1‐parameter subgroups inside ambient Galois‐twisted toric varieties. Over a Henselian field, the resulting tropicalization maps become Galois‐equivariant. We call their images Galois‐equivariant tropicalizations, and use them to construct a large supply of Galois representations in the tropical cellular cohomology groups of Itenberg, Katzarkov, Mikhalkin and Zharkov. We also prove two results which say that under minimal hypotheses on a variety X0 over a Henselian field K0, Galois‐equivariant tropicalizations carry all of the arithmetic structure of X0. Namely, (1) the Galois‐orbit of any point of X0 valued in the separable closure of K0 is reproduced faithfully as a Galois‐set inside some Galois‐equivariant tropicalization of our variety. (2) The Berkovich analytification of X0 over the separable closure of K0, equipped with its canonical Galois‐action, is the inverse limit of all Galois‐equivariant tropicalizations of our variety. [ABSTRACT FROM AUTHOR]

Eshelby proved in 1957 that the strain field within a homogeneous ellipsoidal inclusion embedded in an infinite isotropic media is uniform, when the eigenstrain prescribed in the inclusion is uniform. This uniform strain field property was conjectured to hold exclusively for the ellipsoidally shaped inclusions. In recent studies the authors have discovered the arithmetic mean properties of the strains for N-fold (N is greater than 2 but unequal to 4) rotational symmetrical inclusions with uniform eigenstrains, called the arithmetic mean theorem of the Eshelby tensors. In this paper, we investigate the two-dimensional rotational symmetrical inclusions with rotational symmetrical eigenstrains. It is shown that for N-fold (N is greater than 4) rotational symmetrical inclusions with the same fold rotational symmetrical eigenstrains which are constant on the boundary of the inclusion, the arithmetic mean of the strains at N rotational symmetrical points presents special properties: For the points outside the inclusion, the arithmetic mean vanishes; for the points inside the inclusion, the arithmetic mean is in direct proportion to the eigenstrain on the boundary of the inclusion, with the coefficient tensor equal to the Eshelby tensor for circular inclusions. It is followed that the average strain over the inclusion domain and the line average of strains along a concentric circle inside the inclusion also equal the eigenstrains on the boundary of the inclusion multiplied by the Eshelby tensor for circular inclusions. These properties obtained in this paper can be safely reduced to the results for uniform eigenstrains shown in our former works. [ABSTRACT FROM AUTHOR]

To help guide certain problem‐solving efforts in a timely and relevant manner, public agencies should consider the use of simple multiplicative component models. Such models involve basic algebra, arithmetic, practical logic, and straightforward cross‐tabulations and tables. Two actual case examples are presented. Additional diverse applications are briefly discussed to illustrate the potential value of this tool to guide a number of evidence‐informed efforts. [ABSTRACT FROM AUTHOR]

We take an argument of Gödel's from his ground‐breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: the sentence G says about itself that it is not provable, and G is indeed not provable; therefore, G is true. [ABSTRACT FROM AUTHOR]

The main result of this paper partially answers a question raised in about the existence of countable just recursively saturated models of Peano Arithmetic with non-isomorphic automorphism groups. We show the existence of infinitely many countable just recursively saturated models of Peano Arithmetic such that their automorphism groups are not topologically isomorphic. We also discuss maximal open subgroups of the automorphism group of a countable arithmetically saturated model of [ABSTRACT FROM AUTHOR]

In this paper we study local induction w.r.t. Σ1-formulas over the weak arithmetic [ABSTRACT FROM AUTHOR]

In this paper, we prove that, for any a, M ∈ ℕ with ( a, M) = 1, there are infinitely many Carmichael numbers m such that m ≡ a mod M. [ABSTRACT FROM AUTHOR]

A spring‐damper‐mass system can be used as a passive vibration absorber, which can reduce the vibration amplitudes of a system at certain frequencies or in a broad band. In this paper, a highly efficient computational method called Numerical Assembly Technique (NAT) is extended to vibration problems of beams under arbitrarily distributed loads carrying spring‐damper‐mass systems, to identify the optimal set of parameters of the passive vibration absorbers. The method is quasi‐analytical in the sense that the governing equations are fulfilled exactly and only minor numerical errors due to double‐precision arithmetic are introduced in the boundary and interface conditions. [ABSTRACT FROM AUTHOR]

Abstract: A conjecture of Manin predicts the asymptotic distribution of rational points of bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manin's conjecture for any del Pezzo surface whose Picard rank is sufficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree. [ABSTRACT FROM AUTHOR]

Let χ (mod q) be a primitive Dirichlet character. In this paper, we prove a uniform upper bound of the character sum ∑a∈Aχ(a) over all proper generalized arithmetic progressions A⊂ℤ/q ℤ of rank r: This generalizes the classical result by Pólya and Vinogradov. Our method also applies to give a uniform upper bound for the polynomial exponential sum ∑n∈Aeq(h(n)) (q prime), where h(x)∈ℤ[x] is a polynomial of degree 2≤d

This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects. [ABSTRACT FROM AUTHOR]

This paper suggests an additional channel through which education affects economic growth. If growth is driven by industrialization of production, where machines replace labor in a growing number of tasks, then operating these machines requires workers who are educated, namely literate and know arithmetic, whose human capital is less specific and more general. As a result, technology adoption depends negatively on wages of educated workers. Hence, economic growth depends negatively on the cost of education or on the barriers to acquire education. The model shows that if the cost of education is high, economic growth might be slow and even stop completely, creating a development trap. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to survey the correspondence between bounded arithmetic and propositional proof systems. In addition, it also contains some new results which have appeared as an extended abstract in the proceedings of the conference TAMC 2008 [11]. Bounded arithmetic is closely related to propositional proof systems; this relation has found many fruitful applications. The aim of this paper is to explain and develop the general correspondence between propositional proof systems and arithmetic theories, as introduced by Krajíček and Pudlák [46]. Instead of focusing on the relation between particular proof systems and theories, we favour a general axiomatic approach to this correspondence. In the course of the development we particularly highlight the role played by logical closure properties of propositional proof systems, thereby obtaining a characterization of extensions of EF in terms of a simple combination of these closure properties (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We present some general results concerning the topological space of cuts of a countable model of arithmetic given by a particular indicator Y. The notion of “indicator” is de.ned in a novel way, without initially specifying what property is indicated and is used to de.ne a topological space of cuts of the model. Various familiar properties of cuts (strength, regularity, saturation, coding properties) are investigated in this sense, and several results are given stating whether or not the set of cuts having the property is comeagre. A new notion of “generic cut” is introduced and investigated and it is shown in the case of countable arithmetically saturated models M ⊧ PA that generic cuts exist, indeed the set of generic cuts is comeagre in the sense of Baire, and furthermore that two generic cuts within the same “small interval” of the model are conjugate by an automorphism of the model.The paper concludes by outlining some applications to constructions of cuts satisfying properties incompatible with genericity, and discussing in model-theoretic terms those properties for which there is an indicator Y. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper, we discuss a parabolic system governed by bilinear control, modeled according to Newton's Law. At first we prove that the system is exactly null controllable in long time T > 0 by locally distributed bilinear control and we further prove the exact null controllability in long time T > 0 of the semilinear parabolic equation yt-Δ y + b |∇ y|2=ξοu with traditionally additive locally distributed control and the existence of the control optimal time for the system. Then, we deduce an exact controllability result to particular stationary functions when we are acting over the whole domain and to particular stationary functions vanishing outside some ball included in the control domain when the control domain is as small as we want. [ABSTRACT FROM AUTHOR]