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Let G be a locally compact group. In this short note, we study the space of pseudofunctions, denoted P F Φ (G) , associated with the Orlicz space L Φ (G) , where Φ is a Young function satisfying the Δ 2 -condition. We show that the dual of P F Φ (G) is a commutative Banach algebra. We also study the space of multipliers from the Orlicz Figà–Talamanca Herz algebra A Φ (G) (introduced by the authors in Indag Math 30:340–354, 2019) to the dual of P M Ψ (G) and use it to show that the space of bounded multipliers of A Φ (G) is a dual space. Finally, we characterize the disjointness preserving mappings between two Orlicz Figà–Talamanca Herz algebras. [ABSTRACT FROM AUTHOR]

A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing Nstate coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 2A1 and 1 2E states of the 1-propynyl radical, CH3CC. [ABSTRACT FROM AUTHOR]

Reports on the formulation of pseudo-ensemble simulations and Gibbs-Duhem integrations within the framework of the expanded grand canonical ensemble. Mechanical equilibration achieved by the method faster than both conventional volume moves and canonical simulation of the chemical potential; Coexistence curves for pure homopolymers and polymer mixtures.

Abstract In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. Specifically, the reconstruction of the force is carried out from the estimates of the series coefficients, which in fact are part of the dynamical system that composes the observer. Adams-Bashforth-Moulton method is used to compute the fractional derivatives of the observer in the Liouville-Caputo sense. Experiments based on real data are presented to show the advantages of using a fractional observer in the reconstruction of forces. Highlights • Design of a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system. • Fourier series approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. • Numerical evaluation of the fractional state observer, using experimental data. [ABSTRACT FROM AUTHOR]

In this paper we introduce sigma limits (which we write σ -limits), a concept that interpolates between lax and pseudolimits: for a fixed family Σ of arrows of a 2-category A , a σ -cone for a 2-functor A ⟶ F B is a lax cone such that the structural 2-cells corresponding to the arrows of Σ are invertible. The conical σ-limit of F is the universal σ -cone. Similarly we define σ -natural transformations and weighted σ -limits. We consider also the case of bilimits. We develop the theory of σ -limits and σ -bilimits, whose importance relies on the following key fact: any weighted σ-limit (or σ-bilimit) can be expressed as a conical one . From this we obtain, in particular, a canonical expression of an arbitrary C a t -valued 2-functor as a conical σ -bicolimit of representable 2-functors, for a suitable choice of Σ, which is equivalent to the well known bicoend formula. As an application, we establish the 2-dimensional theory of flat pseudofunctors. We define a C a t -valued pseudofunctor to be flat when its left bi-Kan extension along the Yoneda 2-functor preserves finite weighted bilimits. We introduce a notion of 2-filteredness of a 2-category with respect to a class Σ, which we call σ-filtered . Our main result is: A pseudofunctor A ⟶ C a t is flat if and only if it is a σ-filtered σ-bicolimit of representable 2-functors. In particular the reader will notice the relevance of this result for the development of a theory of 2-topoi. [ABSTRACT FROM AUTHOR]

Aiming at the shortcomings of being rough by using the l 1 norm to replace the original signal for signal reconstruction, this paper first constructs the l 1 norm's smooth approximation function and studies the monotonicity and convergence of the optimal solution sequence. Second, the pseudo-function || x || p (0 <  p  < 1) replaces || x || 1 in signal reconstruction, and the maximum entropy function is used to smooth l p (0 <  p  < 1). In this paper, the algorithm's performance is analyzed and its feasibility is verified using one- and two-dimensional signal reconstruction. This algorithm has smaller error than other compression reconstruction algorithms, better structure, and a more convenient calculation. [ABSTRACT FROM AUTHOR]

We fix any bicategory A together with a class of morphisms W A , such that there is a bicategory of fractions A [ W A − 1 ] (as described by D. Pronk). Given another such pair ( B , W B ) and any pseudofunctor F : A → B , we find necessary and sufficient conditions in order to have an induced pseudofunctor G : A [ W A − 1 ] → B [ W B − 1 ] . Moreover, we give a simple description of G in the case when the class W B is “right saturated”. [ABSTRACT FROM AUTHOR]

LetRbe a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse inR. The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary ∗-ring case by Rakić, Dinčić and Djordjević in 2014. Our definition of pseudo core inverse extends the notion of core inverse to elements of an arbitrary index inR. Meanwhile, it generalizes the notion of core-EP inverse, introduced by Manjunatha Prasad and Mohana for matrices in 2014, to the case of ∗-ring. Some equivalent characterizations for elements inRto be pseudo core invertible are given and expressions are presented especially in terms of Drazin inverse and {1,3}-inverse. Then, we investigate the relationship between pseudo core inverse and other generalized inverses. Further, we establish several properties of the pseudo core inverse. Finally, the computations for pseudo core inverses of matrices are exhibited. [ABSTRACT FROM AUTHOR]

In this paper we define slant submanifolds in neutral almost contact pseudo-metric manifolds, with motivations and examples. We also provide some natural examples of the ambient spaces. [ABSTRACT FROM AUTHOR]

The paper presents a method of instantaneous construction of relative permeability pseudo functions in analytical form upscaled to a coarser computational grid using a system of artificial neural networks. The coefficients of these functions can be forecasted by the neural network. The learning dataset is based on a preliminary series of calculations at the reference values of the system parameters the exponents of the initial functions, the liquid phases viscosity ratio, the statistical parameters of distribution laws of the reservoir's properties. The latter may be obtained according to the primary well logging data with no need for building a detailed geological model. [ABSTRACT FROM AUTHOR]

Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra. [ABSTRACT FROM AUTHOR]

The notion of reduced synthesis in the context of harmonic analysis on general locally compact groups is introduced; in the classical situation of commutative groups, this notion means that a function f in the Fourier algebra is annihilated by any pseudofunction supported on f (0). A relationship between reduced synthesis and compact synthesis (i.e., the possibility of approximating compact operators by pseudointegral ones without increasing the support) is determined, which makes it possible to obtain new results both in operator theory and in harmonic analysis. Applications to the theory of linear operator equations are also given. [ABSTRACT FROM AUTHOR]

We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free ( 4 , 2 ) -categories. In the case of bicategories and pseudofunctors, existing rewriting techniques based on Squier's Theorem allow us to conclude. In the case of pseudonatural transformations this approach only proves the coherence of part of the structure, and we use a new rewriting result to conclude. To this end, we introduce the notions of white-categories and partial coherence. [ABSTRACT FROM AUTHOR]

We show that the class of Banach algebras that can be isometrically represented on an L p -space, for p ≠ 2 , is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study of Banach algebras generated by invertible isometries of L p -spaces. [ABSTRACT FROM AUTHOR]

Geometrical insights are very helpful when learning about the Fourier series. Instead of focusing on trigonometric or exponential functions, we consider a more general collection of orthonormal functions. We show in an elementary way that a Taylor series can also be considered a special case of the generalized Fourier series, with an orthonormal base of power functions and a properly defined inner product. [ABSTRACT FROM AUTHOR]

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an L p -space together with its inverse. Examples include the algebra P F p ( Z ) of p -pseudofunctions on Z , the commutative C ⁎ -algebra C ( S 1 ) and all of its quotients, as well as uncountably many ‘exotic’ Banach algebras. We associate to each isometry of an L p -space a spectral invariant called ‘spectral configuration’, which contains considerably more information than its spectrum as an operator. It is shown that the spectral configuration describes the isometric isomorphism type of the Banach algebra that the isometry generates together with its inverse. It follows from our analysis that these algebras are semisimple. With the exception of P F p ( Z ) , they are all closed under continuous functional calculus, and their Gelfand transform is an isomorphism. As an application of our results, we show that Banach algebras that act on L 1 -spaces are not closed under quotients. This answers the case p = 1 of a question asked by Le Merdy 20 years ago. [ABSTRACT FROM AUTHOR]

An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line. [ABSTRACT FROM AUTHOR]

Let $$S$$ be an inverse semigroup. The space of $$p$$ -pseudomeasures $$\mathop {\mathrm{PM}}_p(S)$$ , introduced in [], is characterized in terms of convolutors of $$l^p(S)$$ when $$S$$ is amenable with finitely many idempotents. Also, when $$\mathrm{A}(S)$$ has a bounded approximate identity with bound $$1$$ , the space of $$\mathrm{A}(S)$$ -multipliers from $$\mathop {\mathrm{VN}}(S)$$ into $$\mathop {\mathrm{VN}}(S)$$ is identified with the dual space of $$\mathop {\mathrm{UC}}(\hat{S})$$ , the closure of $$\mathrm{A}(S)\mathop {\mathrm{VN}}(S)$$ in $$\mathop {\mathrm{VN}}(S)$$ . Then it is shown that $$\mathop {\mathrm{UC}}(\hat{S})$$ is equal to the reduced C $$^*$$ -algebra of $$S$$ . Further, the space of $$p$$ -pseudofunctions $$\mathop {\mathrm{PF}}_p(S)$$ and its dual space $$\mathop {\mathrm{W}}_p(S)$$ are introduced and some properties of them are given. [ABSTRACT FROM AUTHOR]

The article focuses on the research "Quasiglobal Multiphase Upscaling of Reservoir Models With Nonlocal Stratigraphic Heterogeneities." Topics include development of the regional-scale multiphase upscaling (RMU) method to capture nonlocal stratigraphic reservoir elements pseudofunctions for flow simulation, calibration of pseudoization process, dynamic multiphase flow responses of coarse regional-scale sector models, and turbidite stratigraphic architecture numerical.

We present imaging findings of aberrant left gastric vein (ALGV)and associated pseudolesions and mimickers including metastases and focal nodular hyperplasia. ALGV is formed due to interrupted involution of anastomotic omental veins, and it can drain into left portal vein or segments II and III of the liver as third inflow. Focal fat, focal fat sparing, and perfusion changes can be seen due to the presence of ALGV, which can mimic metastasis in cancer patients. ALGV may also serve as a pathway for direct tumor spread into the liver in patients with gastric cancer. Magnetic resonance imaging can be used as a problem solving tool in the presence of equivocal findings on ultrasonography and computed tomography. [ABSTRACT FROM AUTHOR]

Developmental dyslexia is a neurological disorder the underlying biological and cognitive causes of which are still being investigated, a key point, because the findings will determine the best therapeutic approach to use. Using functional magnetic resonance imaging, we studied the brain activation pattern while reading in the language-related cortical areas from the two reading routes, phonological and orthographic, and the strength of their association with reading scores in 66 Spanish-speaking children aged 9-12 years divided into three groups: typically developing readers (controls), dyslexic readers and readers with monocular vision due to ocular motility disorders but with normal reading development, to assess whether (or not) the neuronal network for reading in children with dyslexia has similarities with that in children with impaired binocular vision due to ocular motility disorders. We found that Spanish-speaking children with dyslexia have a brain circuit for reading that differs from that in children with monocular vision. Individuals with dyslexia tend to hypoactivate some of the language-related areas in the left hemisphere engaged by the phonological route, especially the visual word form area and left Wernicke's area, and try to compensate this deficit by activating language-related areas related to the orthographic route, such as the anterior part of the visual word form area and the posterior part of both middle temporal gyri. That is, they seem to compensate for impairment in the phonological route through orthographic routes of both hemispheres. Our results suggest that ocular motility disturbances do not play a causal role in dyslexia. Dyslexia seems to be a neurological disorder that is unrelated to vision impairments and requires early recognition and multidisciplinary treatment, based on improving phonological awareness and language development, to achieve the best possible outcome. [ABSTRACT FROM AUTHOR]

In this paper we introduce two notions --systems of fibrant objects and fibration structures-- which will allow us to associate to a bicategory B a homotopy bicategory Ho(B) in such a way that Ho(B) is the universal way to add pseudo-inverses to weak equivalences in B. Furthermore, Ho(B) is locally small when B is and Ho(B) is a 2-category when B is. We thereby resolve two of the problems with known approaches to bicategorical localization. As an important example, we describe a fibration structure on the 2-category of prestacks on a site and prove that the resulting homotopy bicategory is the 2-category of stacks. We also show how this example can be restricted to obtain algebraic, differentiable and topological (respectively) stacks as homotopy categories of algebraic, differential and topological (respectively) prestacks. [ABSTRACT FROM AUTHOR]

Approximately all of the petroleum reservoirs are heterogeneous, and this heterogeneity exists on all levels from pores to simulation models. Since reservoir data are available on different scales and each property does not measure at the individual level, scale-up must be used for acquiring properties of coarse grid models. One of the most important reservoir properties in multiphase upscaling is relative permeability. Pseudo functions are the main methods for upscaling of relative permeability. Kyte and Berry and transmissibility weighted pseudos are two kinds of dynamic pseudo functions. The Kyte and Berry method is based on Darcy's law and the transmissibility weighted pseudos concentrate on saturation effects rather than pressure effects and uses a transmissibility weighted average for calculation of pseudo relative permeabilities. In this work, the effects of directional inter-block pseudos and well pseudos were first investigated. Then the results of coarse grid simulation with directional transmissibility weighted pseudos and Kyte and Berry pseudos were compared with the reference fine grid results. [ABSTRACT FROM PUBLISHER]

Let f(x) be a smooth strictly convex solution of det(∂² f /∂xi∂xi) = exp {(1/2) Σi=1n xi (∂f /∂xi) - f} defined on a domain Ω ⊂ ℝn; then the graph M∇f of ∇f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space ℝn2n with the indefinite metric Σdxidyi. In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graph M∇f is complete in ℝn2n and passes through the origin then it is flat. [ABSTRACT FROM AUTHOR]

Partially functional broadside tests were defined to address the tradeoff that exists between fault coverage and proximity to functional operation conditions during the application of scan-based tests for delay faults. Proximity to functional operation conditions is important for avoiding overtesting. The definition of a partially functional broadside test does not take into consideration the extent of deviation from functional operation conditions that occurs during the second pattern of a test. The authors define two-dimensional partially functional broadside tests to address this issue. The authors demonstrate through experimental results that this improves the ability of the test to remain close to functional operation conditions during the application of both patterns. [ABSTRACT FROM AUTHOR]

semi-analytical method for upscaling two-phase immiscible flows in heterogeneous porous media is described. This method is developed for stratified reservoirs with perfect communication between layers (the case of vertical equilibrium), in a viscous dominant regime, where the effects of capillary forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure gradient in vertical direction may be set zero, which is the only assumption of our derivation. In this way, the 2D Buckley-Leverett problem may be reduced to a one-dimensional problem for a system of quasi-linear hyperbolic equations, of a number equal to the number of layers in the reservoir. They are solved numerically, based on an upstream finite difference algorithm. Self-similarity of the solution makes it possible to compute pseudofractional flow functions depending on the average saturation. The computer partial differential equation solver COMSOL is used for comparison of the complete 2D solutions with averaged 1D simulations. Cases of both discrete and continuous (log-normal) permeability distribution are studied. Generally, saturation profiles of the 1D model are only slightly different from the 2D simulation results. Recovery curves and fractional flow curves fit well. Calculations show that at a favorable mobility ratio (displaced to displacing phase) crossflow increases the recovery, while at an unfavorable mobility ratio, the effect is the opposite. Compared with the classical Hearn method, our method is more general and more precise, since it does not assume universal relative permeabilities and piston-like displacement, and it presumes non-zero exchange between layers. The method generalizes also the study of Yortsos (Transp Porous Media 18:107-129, ), taking into account in a more consistent way the interactions between the layers. [ABSTRACT FROM AUTHOR]

Abstract: This paper has a two-fold purpose. Let . We first introduce the p-operator space injective tensor product and study various properties related to this tensor product, including the p-operator space approximation property, for p-operator spaces on -spaces. We then apply these properties to the study of the pseudofunction algebra , the pseudomeasure algebra , and the Figà–Talamanca–Herz algebra of a locally compact group G. We show that if G is a discrete group, then most of approximation properties for the reduced group C∗-algebra , the group von Neumann algebra , and the Fourier algebra (related to amenability, weak amenability, and approximation property of G) have the natural p-analogues for , , and , respectively. The p-completely bounded multiplier algebra plays an important role in this work. [Copyright &y& Elsevier]

In this paper, we use the elementary method to study the properties of pseudo Smarandache function Ut(n), and obtain some interesting identities involving function Ut(n), and for any fixed integer n, offer a method of calculating of the infinite series Σ∞ i=1 Ut(n). [ABSTRACT FROM AUTHOR]

A rapid analytical optical biosensor-based immunoassay was developed and validated for the detection of okadaic acid (OA) and its structurally related toxins from shelifish matrix. The assay utilizes a monoclonal antibody which binds to the OA group of toxins in order of their toxicities, resulting in a pseudofunctional assay. Single-laboratory validation of the assay for quantitative detection of OA determined that it has an action limit of 120 μg/kg, a limit of detection of 31 μg/kg, and a working range of 31-174 μg/kg. The midpoint on the standard matrix calibration curve is 80 μg/kg, half the current regulatory limit. Inter- and mu-a-assay studies of negative mussel samples spiked with various OA concentrations produced average coefficient of variation (CV) and standard deviation (SD) values of 7.9 and 10.1, respectively. The assay was also validated to confirm the ability to accurately codetect and quantify dinophysistoxin-1 (DTh-1), DTX-2, and DTX-3 from shellfish matrix. Alkaline hydrolysis was not required for the detection of DIX-3 from matrix. Excellent correlations with the data generated by the biosensor method and liquid chromatography/tandem mass spectrometry (LC/ MS/MS) were obtained using a certified reference material (R2 = 0.99), laboratory reference material, and naturally contaminated mussel samples (R2 = 0.97). This new procedure could be used as a rapid screening procedure replacing animal-based tests for DSP toxins. [ABSTRACT FROM AUTHOR]

Abstract: The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general -spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banach algebras. We use these operator space structures to gain new insights on those algebras. [Copyright &y& Elsevier]

In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate of certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. [ABSTRACT FROM AUTHOR]

Abstract: The approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals. Also they are all linear operators. We address in the present paper the following problems: Need all the approximation operators be linear? Is the linear structure the only one which allows us to construct particular approximation operators? As an answer to this problem we propose new, particular, pseudo-linear approximation operators, which are defined in some ordered semirings. We study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory. In this sense we obtain uniform approximation theorems of Weierstrass type, and Jackson-type error estimates in approximation by these operators. [Copyright &y& Elsevier]

Abstract: We decompose every linear pseudo hoop as an Aglianò–Montagna type of ordinal sum of linear Wajsberg pseudo hoops which are either negative cones of linear -groups or intervals in linear unital -groups with strong unit. We apply the decomposition to present a new proof that every linear pseudo BL-algebra and consequently every representable pseudo BL-algebra is good. Moreover, we show that every maximal filter and every value of a linear pseudo hoop is normal, and every -complete linear pseudo hoop is commutative. [Copyright &y& Elsevier]

Abstract: We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues–Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category. [Copyright &y& Elsevier]

Several multiscale methods for elliptic problems that provide high resolution velocity fields at low computational cost have been applied to porous media flow problems. However, to achieve enhanced accuracy in the flow simulation, the numerical scheme for modeling the transport must account for the fine scale structures in the velocity field. To solve the transport equation on the fine scale with conventional finite volume methods will often be prohibitively computationally expensive for routine simulations. In this paper we propose a more efficient adaptive multiscale method for solving the transport equation. In this method the global flow is computed on a coarse grid scale, while at the same time honoring the fine scale information in the velocity field. The method is tested on both two- and three-dimensional test cases with complex heterogeneous structures. The numerical results demonstrate that the adaptive multiscale method gives nearly the same flow characteristics as simulations where the transport equation is solved on the scale of an underlying fine grid. Some analysis is presented to estimate error sources and support our conclusions from the numerical results. [ABSTRACT FROM AUTHOR]

Recent research results have shown that the traditional structural testing for delay and signal integrity faults may result in overtesting due to the nontrivial number of such faults that are untestable in the functional mode although testable in the test mode. This paper presents a pseudofunctional-test methodology that attempts to minimize the overtesting problem of the scan-based circuits in automatic test pattern generation (ATPG) and built-in self-test (BIST) test generation approaches. The first pattern of a two-pattern test is still delivered by scan in the test mode but the pattern is generated in such a way that it does not violate the functional constraints extracted from the functional logic. The second pattern is then generated in a functional mode using the functional justification (also called broadside) test application scheme. The authors use a sequential boolean satisfiability solver to extract a set of functional constraints that consists of illegal states and internal signal correlation. The functional constraints are imposed upon an ATPG tool to generate pseudofunctional tests and/or implemented as a monitor in the BIST environment to allow only functional-like patterns generated from the random test pattern generator as tests. The experimental results for delay faults indicate that the percentage of functionally untestable delay faults is nontrivial for many circuits. This finding supports the hypothesis of the overtesting problem in delay testing. In addition, the results indicate the effectiveness of the proposed constraint extraction method and the proposed BIST scheme. [ABSTRACT FROM AUTHOR]

Abstract: The Wiener-Ikehara theorem was devised to obtain a simple proof of the prime number theorem. It usesno other information about the zeta function ~(z) than that it is zero-free and analytic for Rez ⩾ 1, apart from a simple pole at z = 1 with residue 1. In the Wiener-Ikehara theorem, the boundary behavior of a Laplace transform in the complex plane plays a crucial role. Subtracting the principal singularity, a first order pole, the classical theorem requires uniform convergence to a boundary function on every finite interval. Here it is shown that local pseudofunction boundary behavior, which allows mild singularities, is necessary and sufficient for the desired asymptotic relation. It follows that the twin-prime conjecture is equivalent to pseudofunction boundary behavior of a certain analytic function. [Copyright &y& Elsevier]

In this paper we define a cohomology theory for an arbitrary K-linear semistrict semigroupal 2-category (C,⊗) (called for short a Gray semigroup) and show that its first-order (unitary) deformations, up to the suitable notion of equivalence, are in bijection with the elements of the second cohomology group. Fundamental to the construction is a double complex, similar to the Gerstenhaber–Schack double complex for bialgebras, the role of the multiplication and the comultiplication being now played by the composition and the tensor product of 1-morphisms. We also identify the cohomologies describing separately the deformations of the tensor product, the associator and the pentagonator. To obtain the above results, a cohomology theory for an arbitrary K-linear (unitary) pseudofunctor is introduced describing its purely pseudofunctorial deformations, and generalizing Yetter''s cohomology for semigroupal functors (in: M. Kapranov, E. Getzler (Eds.), Higher Category Theory, AMS Contemporary Mathematics, Vol. 230, Amer. Math. Soc., Providence, RI, 1998, pp. 117–134). The corresponding higher order obstructions will be considered in detail in a future paper. [Copyright &y& Elsevier]

In this paper we introduce the notion of an extensive 2-category, to be thought of as a “2-category of generalized spaces”. We consider an extensive 2-category K equipped with a binary-product-preserving pseudofunctor C:Kop→CAT, which we think of as specifying the “coverings” of our generalized spaces. We prove, in this context, a van Kampen theorem which generalizes and refines one of Brown and Janelidze. The local properties required in this theorem are stated in terms of morphisms of effective descent for the pseudofunctor C. We specialize the general van Kampen theorem to the 2-category TopS of toposes bounded over an elementary topos S, and to its full sub 2-category LTopS determined by the locally connected toposes, after showing both of these 2-categories to be extensive. We then consider three particular notions of coverings on toposes corresponding, respectively, to local homeomorphisms, covering projections, and unramified morphisms; in each case we deduce a suitable version of a van Kampen theorem in terms of coverings and, under further hypotheses, also one in terms of fundamental groupoids. An application is also given to knot groupoids and branched coverings. Along the way we are led to investigate locally constant objects in a topos bounded over an arbitrary base topos S and to establish some new facts about them. [Copyright &y& Elsevier]

If the subset T supports a synthesizable p-pseudofunction T, then the restriction Ap(E) to E of the Herz algebra on T is not Arens regular. The proof is direct, by brute force, and does not show the existence of Day points for Ap(E). 2000 Mathematics Subject Classification 43A15, 43A10 (primary), 46L10 (secondary). [ABSTRACT FROM PUBLISHER]

Presents information on a simple proof of Ogawa's result on concrete construction of pseudorandom functions. Explanations on theorems; Construction of pseudorandom functions with symmetric stable asymptotic distribution; Derivation of equations.

The nonlinear complementarity problem (NCP) can be reformulated as a system of semismooth equations by some NCP functions. A well-known NCP function is the Fischer-Burmeister function, which is a strongly semismooth function. It is smooth everywhere except at the origin. The generalized Newton direction of the system of semismooth equations formulated with the Fischer-Burmeister function is always a descent direction at a nonsolution point. The generalized Jacobian of the system is nonsingular under mild conditions. Efficient algorithms have been developed based upon these nice properties. In this paper, we define a class of NCP functions, called regular pseudo-smooth NCP functions, and show that they have these nice properties. Regular pseudo-smooth NCP functions can be easily identified. They include the Fischer-Burmeister function, the Tseng-Luo NCP function family, and the Kanzow-Kleinmichel NCP function family. We give two new regular pseudo-smooth NCP function families: the ratio generated NCP function family and the C curve generated NCP function family. We then discuss the box constrained variational inequality problem (BVIP). We define a class of BVIP functions, called regular pseudo-smooth BVIP functions, and show that they have these nice properties too. We present three different approaches to generate regular pseudo-smooth BVIP functions from regular pseudo-smooth NCP functions. Globally and quadratically convergent generalized Newton methods are established for solving the NCP and the BVIP, based upon regular pseudo-smooth NCP and BVIP functions. [ABSTRACT FROM AUTHOR]

Large-scale averaging is important for the description of displacement processes in heterogeneous porous media. For immiscible displacement, a key objective is the determination of effective (pseudo) capillary pressure and phase permeabilities. Present continuum models rely on volume averaging, mixture theories, and homogenization methods, typically under the premise of capillary control. However, such methods are intrinsically unable to provide the local saturation distribution, which is needed for the computation of effective flow properties. In this paper, paralleling pore-level approaches, a percolation method is proposed for the derivation of large-scale properties in a drainage process at low flow rates. Percolation concepts are applied to a macroscopically heterogeneous region with a random and uncorrelated permeability distribution. Appropriate modifications of ordinary and invasion percolation, and percolation with trapping are developed for the determination of the large scale averages. Analytical results are also presented for certain simple cases. We show that for drainage at conditions of local capillary control, when a local description is possible, the large-scale capillary pressure curve is a nontrivial average of the individual curves. Large scale capillary trapping is predicted and a corresponding large-scale trapped saturation is calculated. Large-scale phase premeabilities are also derived. It is found that capillary heterogeneity renders a system more strongly wet in a macroscopic sense. The results are applicable to drainage, but not to imbibition, where a different mode of penetration holds. [ABSTRACT FROM AUTHOR]

The band structure of Bi2Ru2O7 and Pb2Ru2O6.5 has been computed self-consistently from first principles for the first time by the pseudofunction method. We discover that the 6s bands of Bi and Pb are very deep and unlikely to contribute to the metallic behavior as previously believed. The unoccupied 6p bands, however, are only several eV above the Fermi energy and are mixed with the Ru 4d band at the Fermi surface via the framework O atoms, leading to band conduction and delocalized magnetic moments. The predicted location of the 6s bands and the location and width of the O 2p band are confirmed by synchrotron radiation and ultraviolet electron spectroscopy of single crystals. [ABSTRACT FROM AUTHOR]