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Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s in N, we determine K_mE/p^sK_mE as a (Z/p^sZ)[Gal(E/F)]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero.

73 pages ; 25 cm

This registration archives Version 1.0/1.1 of the core PET Module 0.0 definitions, establishing the dual-layer pulse concept (Cosmic Prototype and Instance Pulse) for the Pulsating Energy Theory as of May 9, 2025. Files included: PET-M0.0-A_CosmicPrototype_v1.0.pdf, PET-M0.0-B_InstancePulse_v1.1.pdf, PET-M0.0_Clarification_Context_v1.0.pdf.

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,\]where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".

We extend a result of Napp Avelli, van der Put, and Rocha with a system-theoretic interpretation to the noncommutative case: Let P be a f.g. projective module over a two-sided Noetherian domain. If P admits a subdirect product structure of the form P = M x_T L over a factor module T of grade at least 2 then the torsion-free factor of M (resp. L) is projective.

Let $G=SU(2)$ and let $\Omega G$ denote the space of based loops in SU(2). We explicitly compute the $R(G)$-module structure of the topological equivariant $K$-theory $K_G^*(\Omega G)$ and in particular show that it is a direct product of copies of $K^*_G(\pt) \cong R(G)$. (We intend to describe in detail the $R(G)$-algebra (i.e. product) structure of $K^*_G(\Omega G)$ in a forthcoming companion paper.) Our proof uses the geometric methods for analyzing loop spaces introduced by Pressley and Segal (and further developed by Mitchell). However, Pressley and Segal do not explicitly compute equivariant $K$-theory and we also need further analysis of the spaces involved since we work in the equivariant setting. With this in mind, we have taken this opportunity to expand on the original exposition of Pressley-Segal in the hope that in doing so, both our results and theirs would be made accessible to a wider audience.

Korps Lalu Lintas Kepolisian Republik Indonesia (Korlantas Polri) menerbitkan buku panduan ujian teori SIM sebagai sarana pembelajaran tentang pengetahuan, tata tertib dan etika berlalu lintas bagi masyarakat yang akan mengikuti ujian teori SIM. Buku ini merupakan edisi perdana yang terbit pada tahun 2023. Isi buku terdiri dari pengantar instrumen perlengkapan jalan yang meliputi rambu, marka, dan Alat Pemberi Sinyal Lalu Lintas (APILL); pengantar kendaraan yang menjelaskan tentang komponen dan perlengkapan kendaraan; dan ulasan soal serta pembahasan ujian teori SIM yang berisi materi tentang persepsi bahaya, wawasan, dan pengetahuan dalam berlalu lintas. Dengan hadirnya buku ini diharapkan dapat menjawab harapan masyarakat dan menjadi solusi atas minimnya sarana pembelajaran dalam berlalu lintas dengan baik dan benar sehingga dapat membentuk karakter pengendara yang aman. Semoga ikhtiar ini dapat memberikan kontribusi nyata sebagai wujud pengabdian Polri kepada masyarakat, bangsa dan negara.

This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of $P(z)$-tensor products for nonzero complex numbers $z$ constructed in Part III of the present series under suitable conditions. The associativity isomorphisms constructed in this paper are analogous to associativity isomorphisms for vector space tensor products in the sense that it relates the tensor products of three elements in three modules taken in different ways. The main new feature is that they are controlled by the decompositions of certain spheres with four punctures into spheres with three punctures using a sewing operation. We also show that under certain conditions, the existence of the associativity isomorphisms is equivalent to the associativity (or (nonmeromorphic) operator product expansion in the language of physicists) for the intertwining operators (or chiral vertex operators). Thus the associativity of tensor products provides a means to establish the (nonmeromorphic) operator product expansion.

Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a meromorphic parameter $\lambda$, especially its Laurent expansion and integration, from an algorithmic viewpoint in the framework of $D$-module theory.

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.

The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.

This manual presents a self-instructional program designed to acquaint educators with general systems theory as it applies to instructional development practices and the diffusion of instructional innovations. It is also intended to provide an intellectual and emotional frame of reference for individuals undertaking instructional development activities and to present a checklist of criteria and/or operations related to systematic instructional development. The manual was originally developed as part of the materials for participants at the Instructional Development Institute, but it was also designed for use by school personnel who did not attend the institute. The manual is organized in three sections that correspond to the three stages of the instructional development model--(1) identifying the problem, (2) analyzing the setting, and (3) organizing management. Short summary "guideposts" are interspersed throughout the program, and frequent references are made to the variety of supplemental and exemplary materials contained in the appendix. (JG)

This is a rough module( teaching material) that  helps a students at higher education.

We test the umbral methods introduced by Rota and Taylor within the theory of representation of symmetric group. We define a simple bijection between the set of all parking functions of length $n$ and the set of all noncrossing partitions of $\{1,2,...,n\}$. Then we give an umbral expression of the Frobenius characteristic of the parking function module introduced by Haiman that allows an explicit relation between this symmetric function and the volume polynomial of Pitman and Stanley.

In this paper we describe and continue the study begun by the author, Jones, and Segal, of the homotopy theory that underlies Floer theory. In that paper the authors addressed the question of realizing a Floer complex as the celluar chain complex of a CW -spectrum or pro-spectrum, where the attaching maps are determined by the compactified moduli spaces of connecting orbits. The basic obstructions to the existence of this realization are the smoothness of these moduli spaces, and the existence of compatible collections of framings of their stable tangent bundles. In this note we describe a generalization of this, to show that when these moduli spaces are smooth, and are oriented with respect to a generalized cohomology theory E^*, then a Floer E_* -homology theory can be defined. In doing this we describe a functorial viewpoint on how chain complexes can be realized by E -module spectra, generalizing the stable homotopy realization criteria given earlier by the author, Jones, and Segal. Since these moduli spaces, if smooth, will be manifolds with corners, we give a discussion about the appropriate notion of orientations of manifolds with corners.

This module is the fourth of five integrated professional development modules for adult literacy and basic education (ALBE) personnel. This module is in the form of a 6-hour workshop, the purposes of which are to develop further the practitioners' knowledge of the theoretical basis of teaching literacy in ALBE programs, to provide a supportive adult learning environment in which practitioners can think critically about their own knowledge and understanding of theory, and to encourage practitioners to define good practice in relation to current and endorsed theory and to reflect critically on their own practice. An overview consists of these components: duration, purpose, relationship to competency standards, prerequisites and/or corequisites, summary of content, delivery, list of learning outcomes, assessment criteria, minimum essential resources, and suggested references. Presenter's guidelines correlate content to the guidelines and resources in a three-column table format. The workshop resources section contains handouts, transparency masters, suggested resources, and workshop evaluation form. (YLB)

This main purpose of this article is the unification of the Galois theory of algebraic differential equations by Umemura and the Galois theory of algebraic difference equations by Morikawa-Umemura in a common framework using Artinian simple D-module algebras, where D is a bialgebra. We construct the Galois hull of an extension of Artinian simple D-module algebras and define its Galois group, which consists of infinitesimal coordinate transformations fulfilling certain partial differential equations and which we call Umemura functor. We eliminate the restriction to characteristic 0 from the above mentioned theories and remove the limitation to field extensions in the theory of Morikawa-Umemura, allowing also direct products of fields, which is essential in the theory of difference equations. In order to compare our theory with the Picard-Vessiot theory of Artinian simple D-module algebras due to Amano and Masuoka, we first slightly generalize the definition and some results about them in order to encompass as well non-inversive difference rings. Finally, we give equivalent characterizations for smooth Picard-Vessiot extensions, describe their Galois hull and show that their Umemura functor becomes isomorphic to the formal scheme associated to the classical Galois group scheme after a finite \'etale base extension.

This interactive module contains 33 windows of text and three graphics, in which Freud's topographical (unconscious, pre-conscious, and conscious) and structural (id, ego, and superego) models of the psyche are studied. Seventeen fill-in questions are interspersed within the text. The module stresses the importance of comprehending the concept of unconscious motivation as a key towards understanding human behavior. The psychodynamic character of the mind is also equally stressed with various examples. (Author)

This interactive module contains 33 windows of text and three graphics, in which Freud's topographical (unconscious, pre-conscious, and conscious) and structural (id, ego, and superego) models of the psyche are studied. Seventeen fill-in questions are interspersed within the text. The module stresses the importance of comprehending the concept of unconscious motivation as a key towards understanding human behavior. The psychodynamic character of the mind is also equally stressed with various examples. (Author)

Recently, Duncan and Mack-Crane established an isomorphism, as Virasoro modules at central charges c=12, between the space of states of the Conway Moonshine Module and the space of states of a special K3 theory that was extensively studied some time ago by Gaberdiel, Volpato and the two authors. In the present work, we lift this result to the level of modules of the extensions of these Virasoro algebras to N=4 super Virasoro algebras. Moreover, we relate the super vertex operator algebra and module structure of the Conway Moonshine Module to the operator product expansion of the K3 theory by a procedure we call reflection. This procedure can be applied to certain superconformal field theories, transforming all fields to holomorphic ones. Vice versa, it allows to describe certain superconformal field theories entirely within the language of super vertex operator algebras. We discuss reflection and its limitations in general, and we argue that by reflection, the Conway Moonshine Module inherits from the K3 theory a richer structure than anticipated so far. The comparison between the Conway Moonshine Module and the K3 theory is considerably facilitated by exploiting the free fermion description as well as the lattice vertex operator algebra description of both theories. We include an explicit construction of cocycles for the relevant charge lattices, which are half integral. The transition from the K3 theory to the Conway Moonshine Module via reflection promotes the latter to the role of a medium that collects the symmetries of K3 theories from distinct points of the moduli space, thus uncovering a version of symmetry surfing in this context.

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show that this formulation of the conjecture can be applied to crossed product rings R*G equipped with twisted involutions and automatically implies the a priori more general fibered version.

We overview numerous algorithms in computational $D$-module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Singular}. We discuss new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of polynomials. We analyze algorithms for local Bernstein-Sato polynomials and also algorithms, recovering any kind of Bernstein-Sato polynomial from partial knowledge of its roots. We address a novel way to compute the Bernstein-Sato polynomial for an affine variety algorithmically. All the carefully selected nontrivial examples, which we present, have been computed with our implementation. We address such applications as the computation of a zeta-function for certain integrals and revealing the algebraic dependence between pairwise commuting elements.

We define a Dieudonn\'e module as the module of Dieudonn\'e elements, and set up Dieudonn\'e module theory in a simple way. Under this formulation we give explicit formulae for the duality and the corresponding differential operators.

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely represent the submanifolds. For example, the analytic index of Dirac operator of a space curve is identified with its writhing number. As another example, the operator determinants of the Dirac operators are closely related to invariances of the immersed objects, such as Euler-Bernoulli and Willmore functionals for a space curve and a conformal surface respectively. In this article, we will give mathematical construction of the Dirac operator by means of $\Cal D$-module and reformulate my recent results mathematically.

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely represent the submanifolds. For example, the analytic index of Dirac operator of a space curve is identified with its writhing number. As another example, the operator determinants of the Dirac operators are closely related to invariances of the immersed objects, such as Euler-Bernoulli and Willmore functionals for a space curve and a conformal surface respectively. In this article, we will give mathematical construction of the Dirac operator by means of $\Cal D$-module and reformulate my recent results mathematically.

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely represent the submanifolds. For example, the analytic index of Dirac operator of a space curve is identified with its writhing number. As another example, the operator determinants of the Dirac operators are closely related to invariances of the immersed objects, such as Euler-Bernoulli and Willmore functionals for a space curve and a conformal surface respectively. In this article, we will give mathematical construction of the Dirac operator by means of $\Cal D$-module and reformulate my recent results mathematically.

Techniques are being developed to gain understanding of energy transport efficiencies through changes in pulsed power transmission line geometries. These techniques are being applied to a design study of the PBFA-II accelerator which has the goal of increasing the energy available for ICF experiments.

We consider D-branes in string theory and address the issue of how to describe them mathematically as a fundamental object (as opposed to a solitonic object) of string theory in the realm in differential and symplectic geometry. The notion of continuous maps, $k$-times differentiable maps, and smooth maps from an Azumaya/matrix manifold with a fundamental module to a (commutative) real manifold $Y$ is developed. Such maps are meant to describe D-branes or matrix branes in string theory when these branes are light and soft with only small enough or even zero brane-tension. When $Y$ is a symplectic manifold (resp. a Calabi-Yau manifold; a $7$-manifold with $G_2$-holonomy; a manifold with an almost complex structure $J$), the corresponding notion of Lagrangian maps (resp. special Lagrangian maps; associative maps, coassociative maps; $J$-holomorphic maps) are introduced. Indicative examples linking to symplectic geometry and string theory are given. This provides us with a language and part of the foundation required to study themes, new or old, in symplectic geometry and string theory, including (1) $J$-holomorphic D-curves (with or without boundary), (2) quantization and dynamics of D-branes in string theory, (3) a definition of Fukaya category guided by Lagrangian maps from Azumaya manifolds with a fundamental module with a connection, (4) a theory of fundamental matrix strings or D-strings, and (5) the nature of Ramond-Ramond fields in a space-time. The current note D(11.1) is the symplectic/differential-geometric counterpart of the more algebraic-geometry-oriented first two notes D(1) ([L-Y1]) (arXiv:0709.1515 [math.AG]) and D(2) ([L-L-S-Y], with Si Li and Ruifang Song) (arXiv:0809.2121 [math.AG]) in this project.

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a ``complex analogue'' of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. The theory applies in particular to many familiar ``rational'' vertex operator algebras, including those associated with WZNW models, minimal models and the moonshine module. In this paper (Part I), we introduce the notions of $P(z)$- and $Q(z)$-tensor product, where $P(z)$ and $Q(z)$ are two special elements of the moduli space of spheres with punctures and local coordinates, and we present the fundamental properties and constructions of $Q(z)$-tensor products.

In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every derivation X a module parallel transport, which is a lift to the module of the one-parameter group of algebra automorphisms generated by X. This parallel transport morphism is determined uniquely by an ordinary differential equation depending on the covariant derivative along X. Based on these parallel transport morphisms, we define a basic set of gauge invariant observables, i.e. functions from the space of connections to the complex numbers. For modules equipped with a hermitian structure, we prove that this set of observables is separating on the space of gauge equivalence classes of hermitian connections. This solves the gauge copy problem for fuzzy gauge theories.

The use of crack growth analysis tools based on plasticity-induced crack closure model, such as FASTRAN, CGAP and AFGROW, requires the conversion of crack growth rate versus the nominal stress intensity range curves to a 'single' curve of crack growth rate versus the effective stress intensity range. In order to minimise the error arising from crack growth rate conversion and judicially utilise these software tools, a user-friendly tool was integrated into CGAP. This report documents the theory, implementation, the user guide and examples of the crack growth rate conversion software module.

From the bitsavers.org collection, a scanned-in computer-related document. waveMate :: Jupiter :: WaveMate CPU-125 Central Processor Unit Module Theory and Operation Manual 1976

Unit III Free modules over PID’s, Invariant factor theorem for sub modules, Finitely generated  modules over PID, Chain of invariant ideals, Fundamental structure theorem for finitely  generated module over a PID,  Unit IV Projective and injective modules, Divisible group.

Business students may dream of receiving pay packages like that of Michael Eisner at Disney. However, many of them will work for the compensation consultant who determines the economics of the pay arrangements, for the valuation consultant who values the different components of the pay arrangements, for the accountant who must audit the financial statement impacts of the pay arrangements, or as a manager in the company whose employees respond to the incentives provided by the pay arrangements. No matter their eventual role, it is critical that every student understands these various aspects of executive pay arrangements, and how these practices have evolved over time. The course module presented herein is designed to effectively integrate these perspectives in as few as five or as many as nine 80-minute sessions that could be a substantive component of an MBA or Master of Accounting capstone course, or a component of a corporate governance elective. A case based on the CEO compensation of Boeing Inc. over the last 60 years provides a series of assignments that effectively integrate the module.

This paper discusses two related areas in which recent advancements in cognitive science and educational technology may affect instructional design theory. These are: (1) the analysis of information-to-be-learned; and (2) the linkage of learning theory to instructional prescriptions. The first area proposes extensions to current methods of content/task analysis procedures. Contextual module analysis proposes an additional analysis of the information based upon complex problems associated with a given situation. Whereas conventional content and task analyses identify the attributes of the information, the contextual module analysis identifies the organization and accessibility of the information in reference to a given situation. The second area proposes the framework for an instructional design model that links cognitive learning theories with specific educational strategies. Rather than acquisition of knowledge in nonsense isolation, it is proposed that learners acquire knowledge within meaningful situations. Research in instructional design theory has focused on strategies associated with declarative and procedural knowledge with minimal empirical work for strategies associated with contextual knowledge. Instructional technology should provide the means by which cognitive science can be applied to improvements in learning. (31 references) (DB)

As a replacement of the conventional staff-guided group tour for new students at Mercer County Community College, a self-guided tour method was developed. This method utilized a recorded cassette tape and number coded floor plan. With this method, students can be oriented in a meaningful way within their library, at their own pace with no loss of class time. Appendices include a classroom survey form, a questionnaire for new students and an evaluation form for the tour. (Author/AP)

Let H be a semisimple finite dimensional Hopf algebra over a field F of zero characteristic. We prove three major theorems: 1. The Representability theorem which states that every H-module (associative) F-algebra W satisfying an ordinary PI, has the same H-identities as the Grassmann envelope of an $H\otimes\left(F\mathbb{Z}/2\mathbb{Z}\right)^{*}$-module algebra which is finite dimensional over a field extension of F. 2. The Specht problem for H-module (ordinary) PI algebras. That is, every H-T-ideal $\Gamma$ which contains an ordinary PI contains H-polynomials $f_{1},...,f_{s}$ which generates $\Gamma$ as an H-T-ideal. 3. Amitsur's conjecture for H-module algebras, saying that the exponent of the H-codimension sequence of an ordinary PI H-module algebra is an integer.

We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the ``compatibility condition'' in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory.

We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally finitely generated over the ground ring.

Let E be a cyclic extension of degree p^n of a field F of characteristic p. Using arithmetic invariants of E/F we determine k_mE, the Milnor K-groups K_mE modulo p, as Fp[Gal(E/F)]-modules for all m in N. In particular, we show that each indecomposable summand of k_mE has Fp-dimension a power of p. That all powers p^i, i=0,1,...,n, occur for suitable examples is shown in a subsequent paper [MSS2], where additionally the main result of this paper becomes an essential induction step in the determination of K_mE/p^sK_mE as (Z/p^sZ)[Gal(E/F)]-modules for all m, s in N.

This work is dedicated to give the interested reader a good review and background in recent developments in the field of neutrosophic algebraic module theory.

This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a ``complex analogue'' of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. In this paper, we focus on a particular element $P(z)$ of a certain moduli space of three-punctured Riemann spheres; in general, every element of this moduli space will give rise to a notion of tensor product, and one must consider all these notions in order to construct a vertex tensor category. Here we present the fundamental properties of the $P(z)$-tensor product of two modules for a vertex operator algebra. We give two constructions of a $P(z)$-tensor product, using the results, established in Parts I and II of this series, for a certain other element of the moduli space. The definitions and results in Part I (hep-th/9309076, which has been replaced by a new version with a greatly expanded introduction and updated references) and Part II (hep-th/9309159) are recalled.

We study intersection theory on the relative Hilbert scheme of a family of nodal-or-smooth curves, over a base of arbitrary dimension. We introduce an additive group called 'discriminant module', generated by diagonal loci, node scrolls, and twists thereof, and determine the action of the discriminant or big diagonal divisor on this group by intersection. We show that this suffices to determine arbitrary polynomials in Chern classes, in particular Chern numbers, for the tautological vector bundles on the Hilbert schemes, which are closely related to enumerative geometry. The latest version includes some new explicit computations and reference to a computer program due to G. Liu implementing our intersection calculus.

We study intersection theory on the relative Hilbert scheme of a family of nodal-or-smooth curves, over a base of arbitrary dimension. We introduce an additive group called 'discriminant module', generated by diagonal loci, node scrolls, and twists thereof, and determine the action of the discriminant or big diagonal divisor on this group by intersection. We show that this suffices to determine arbitrary polynomials in Chern classes, in particular Chern numbers, for the tautological vector bundles on the Hilbert schemes, which are closely related to enumerative geometry. The latest version includes some new explicit computations and reference to a computer program due to G. Liu implementing our intersection calculus.

The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

The emphasis is on so-called "best solution" problems to questions that frequently arise in practical situations, such as finding an answer for the least amount of time, greatest volume, least amount of work, maximum profit, and minimum cost. One of this module's purposes is to help users become acquainted with the types of calculations necessary to solve such real-world problems. The material looks at: A) Minimum Cost Problem in Industry; B) A Maximum Profit Problem; C) Snell's Law-Light Refraction; D) Surface Area of a Bee's Cell, and E) Arterial Branching. Exercises and a model exam are included, with an answer key to both provided. (MP)

02 Oct 2015 Literature in Theory - Module Introduction

KAU Faculty of Medicine 3rd year CNS MODULE PHYSIOLOGY lecture

Given a Galois cover of curves over $\mathbb{F}_p$, we relate the $p$-adic valuation of epsilon constants appearing in functional equations of Artin L-functions to an equivariant Euler characteristic. Our main theorem generalises a result of Chinburg from the tamely to the weakly ramified case. We furthermore apply Chinburg's result to obtain a `weak' relation in the general case. In the Appendix, we study, in this arbitrarily wildly ramified case, the integrality of $p$-adic valuations of epsilon constants.