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A criterion for the ultrametricity of pretangent spaces to general metric spaces is obtained. [ABSTRACT FROM AUTHOR]

Self-weight stresses in an isotropic horizontal layer are studied using specific finite elements. In the problem, the material is assumed as non-linear with the stress-strain relationship of hyperbolic type and the failure stress determined by Coulomb-Mohr law. The difficulty of the problem consists in the fact that the limit stress depends itself on the unknown stress distribution, so a stress-strain equation cannot be written in an explicit form from the outset. This difficulty is avoided by the method of iteration: a suitable initial stress distribution is supposed and, knowing the material properties, the new stress distribution (appearing as a result of slow gradual weight application) can be found which is taken as the initial for the next iteration, and so on. An importance of the suggested solution consists in the possibility of further study of the layer's dynamic behavior: the found stress distribution allows determining the material properties which should be used in a non-linear dynamic problem. [ABSTRACT FROM AUTHOR]

In this paper, a new approach for the sensitivity analysis of microwave filter networks is presented. It is shown that the standard method of sensitivity calculation based on a tuned filter is only valid for infinitesimal geometry changes and not meaningful for practical tolerance values. However, when the sensitivity calculation is expanded to also include sensitivities of detuned filters, it is shown that accurate tolerance predictions can be made even for large geometry variations. It is found that sensitivities can be related to the stored energy distribution in the filter. Transversal and ladder network-type topologies are examined, and it is demonstrated for the first time that, for in-line topologies, sensitivity can be predicted directly from the group delay of the filter in Chebyshev filters. In order to demonstrate the usefulness of the results obtained, the maximum degradation of the in-band performance has been directly obtained from the group delay for different inline filters. [ABSTRACT FROM AUTHOR]

We identify dglas that control infinitesimal deformations of the pairs (manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover known descriptions of first order deformations and we refine known results on obstructions. Secondly we prove that the Hitchin map is induced by a natural L∞-morphism and, by standard facts about L∞-algebras, we obtain new conditions on obstructions to deform Hitchin pairs. [ABSTRACT FROM AUTHOR]

Abstract: Using the method of analytic continuation in an equivariant differential geometric setting, we exhibit two interesting families of vanishing angular momentum periodic orbits for the Newtonian three-body problem with non-uniform mass distributions having two equal masses which connect at the celebrated figure-8 orbit, exhibited by A. Chenciner and R. Montgomery (2000) in the case of equal masses, and yield a continuous family of periodic three-body motions in the plane. At one end of the family, when the two equal masses are infinitesimal and the third one reaches the value of +1, we arrive at a solution of a double Kepler problem; at the other end of the family, when the third mass is infinitesimal, we have a special case of periodic solution of a restricted three-body problem. [Copyright &y& Elsevier]

The work is devoted to Computability logic (CoL)—the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth by computability in its underlying semantics. This article elaborates some basic complexity theory for the CoL framework. Then it proves soundness and completeness for the deductive system CL12 with respect to the semantics of CoL, including the version of the latter based on polynomial time computability instead of computability-in-principle. CL12 is a sequent calculus system, where the meaning of a sequent intuitively can be characterized as ‘the succedent is algorithmically reducible to the antecedent’, and where formulas are built from predicate letters, function letters, variables, constants, identity, negation, parallel and choice connectives and blind and choice quantifiers. A case is made that CL12 is an adequate logical basis for constructive applied theories, including complexity-oriented ones. MSC: primary: 03F50; secondary: 03D75; 03D15; 03D20; 68Q10; 68T27; 68T30. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the schrödinger equation in a given α - dimensional fractional space with a columb potential depending on a parameter and obtain explicit solution of second order linear ordinary differential equation. [ABSTRACT FROM AUTHOR]

An infinitesimal dipole model (IDM) for an antenna including mutual coupling is used to model the radiation patterns of aperiodic arrays. Each radiating element is modelled by a set of infinitesimal dipoles. The mutual coupling between the elements is calculated and the far field radiation pattern of the antenna is computed in a fast and efficient manner. An invasive weed optimisation algorithm is employed to find both the IDMs and the aperiodic array. The simulation results using IDM are verified with a full-wave analysis. [ABSTRACT FROM AUTHOR]

In this paper we study a Dirichlet optimal control problem for a nonlinear monotone equation with degenerate weight function and with the coefficients which we adopt as controls in L∞(Ω). Since these types of equations can exhibit the Lavrentieff phenomenon, we consider the optimal control problem in coefficients in the so-called class of H-admissible solutions. Using the direct method of calculus of variations we discuss the solvability of the above optimal control problem, and prove the attainability of H-optimal pairs via optimal solutions of some nondegenerate perturbed optimal control problems. We also introduce the concept of the Mosco-stability for the above optimal control problem and study the variational properties of Mosco-stable problems with respect to the special type of domain perturbations. [ABSTRACT FROM AUTHOR]

Motivated by a profound observation of A'Campo we investigate the behaviour of the curvature of f(z,w) = c, f ∊ C{z;w}, |c| small, along infinitesimals. We use the language of infinitesimals as introduced in [2]. Along the way we introduce the important notion of gradient canyon, and prove several theorems in which this notion plays the key role. In this paper we give three such theorems and mention several other facts, to be published elsewhere. [ABSTRACT FROM AUTHOR]

We study some properties of pretangent spaces describing the infinitesimal geometry of general metric spaces. The necessary and sufficient conditions characterizing Ptolemaic pretangent spaces and pretangent spaces, where every three points are situated 'on a single straight line,' are found. As a corollary, we obtain a criterion of embeddability of pretangent spaces into the set ℝ of real numbers endowed by the natural metric. [ABSTRACT FROM AUTHOR]

Abstract: We prove analogues of some of Kostantʼs theorems for infinitesimal Cherednik algebras of . As a consequence, it follows that in positive characteristic the Azumaya and smooth loci of the center of these algebras coincide. [Copyright &y& Elsevier]

Abstract: We estimate effective radii of a spherical nanoindenter at various indentation depths using Hertz elastic contact theory for the fully elastic contact region and AFM profiling residual indentation marks for the elastoplastic contact region. Using frame compliance measured as a function of indentation depth and the concept of infinitesimal deformation of a spherical nanoindenter, we introduce a profile of indentation–depth-dependent frame compliance that successfully explains the variation in frame compliance over the entire contact region. After using this indentation–depth-dependent frame compliance, we evaluated more consistent indenter radii from Hertz elastic contact theory at shallow indentation depths (<90nm). [Copyright &y& Elsevier]

The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (▶) and left (◀) product interacting respectively with the right (/) and left (\) residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL- is a weaker variant of DNL restricted to fa-structures of order ⩽ 1. When axiomatized by means of introduction/elimination rules for / and \, it shows a perfect analogy to NL which DNL lacks. [ABSTRACT FROM AUTHOR]

The article offers information on the proposed methods for identification of all units in reference set of data envelopment analysis (DEA) models. It discusses the use of BCC model in the proposed methods due to the model's capability to approximate different model from DEA models. It adds that infinitesimal constant ε was not used as the method expects each model to be solved in two stages; thus, separate weakly efficient and efficient units. It mentions that strong complementary slackness conditions (SCSC) of linear programming was used to obtain vertices of every DEA model faces. It also highlights the production of strange results under SCSC model due to the rising model size, economic interpretation constraints, and risk of producing incorrect results.

Abstract: We construct flat 3-webs via semi-simple geometric Frobenius manifolds of dimension three and give geometric interpretation of the Chern connection of the web. These webs turned out to be biholomorphic to the characteristic webs on the solutions of the corresponding associativity equation. We show that such webs are hexagonal and admit at least one infinitesimal symmetry at each singular point. Singularities of the web are also discussed. [Copyright &y& Elsevier]

In the present paper, we study the various useful methods of solving the one-dimensional integral equation of Fredholm type. We first solve an integral equation involving the product of multivariable H-function by the application of fractional calculus theory. Further the Fredholm integral equation involving the product of I-functions in the kernel is also considered by the Mellin transform techniques. The results obtained here are general in nature and capable of yielding a large number of results (new or known) hitherto scattered in the literature. [ABSTRACT FROM AUTHOR]

Let F be a tangent to the identity diffeomorphism in (ℂ2,0) and X its infinitesimal generator. We prove that Camacho and Sad’s formal invariant curves of X give summable formal power series, whose sums correspond to the parabolic curves found by Hakim for F and F−1. [ABSTRACT FROM PUBLISHER]

The analysis of the capture zone of wells is useful to design pumping systems and wellhead protection programs. In this study, an analytical solution for the head distribution of a partially penetrating well, and semi-analytical methods to determine the geometry of the capture surface are presented. The analytical solution is derived based on an infinitesimal radius under a constant pumping rate in a two-zone confined aquifer. Using the developed solution, a sensitivity analysis is performed to study the influence of skin on the drawdown, location of the stagnation point, maximum horizontal and vertical extent of the capture surface. The results show the efficiency of a partially penetrating well in the plume removal process is different for positive and negative skins. Also it can be concluded, the skin effect will decrease as the degree of penetration and pumping discharge of the well increase. Generally, the thickness of the skin zone is an influential factor in well hydraulics and hydraulic head distribution. However, it can be seen where the skin zone is less than some specific values, the skin effect is not a significant factor, thus, the geometry of the capture surface can be obtained by assuming a single-zone aquifer. Moreover, the effects of different parameters (pumping rates, degree of penetration of the well, thickness of the skin zone, etc.) on the capture zone are studied. [ABSTRACT FROM AUTHOR]

Due to the great variety of geological and hydro-geological conditions and to exploitation methods, the water inrushes in mines vary in a wide range. The main source of underground water is atmospheric precipitations, as well as water from rivers and lakes that go through the permeable rocks underground. A part of the underground water can come from deliberate introduction of water in case of hydraulic dumps or for other necessities (drinking water for the staff, dust suppression etc.). In a mine there can be main and auxiliary pumping stations that direct water towards the principal collecting and decanting basins. The main (central water evacuation stations are usually found in the immediate vicinity of the main extraction shaft, which can also be used for water evacuation. The mud evacuation installation is situated at level 400 in an annex of the main pumping station at shaft No. 12 and it is intended to remove mud from the water collecting basins. The paper presents the calculus of the acceleration and mechanical strain in the traction and balancing cable of the installation, necessary to determine the strains. [ABSTRACT FROM AUTHOR]

We determine spectrum and eigenspaces of some families of Spin핔 Dirac operators over the flat 3-torus. Our method relies on projections onto appropriate 2-tori on which we use complex geometry. Furthermore we investigate those families by means of spectral sections (in the sense of Melrose/Piazza). Our aim is to give a hands-on approach to this concept. First we calculate the relevant indices with the help of spectral flows. Then we define the concept of a system of infinitesimal spectral sections which allows us to classify spectral sections for small parameters R up to equivalence in K-theory. We undertake these classifications for the families of operators mentioned above. Our aim is therefore twofold: On the one hand we want to understand the behavior of Spin핔 Dirac operators over a 3-torus, especially for situations which are induced from a 4-manifold with boundary T³. This has prospective applications in generalized Seiberg-Witten theory. On the other hand we want to make the term "spectral section", for which one normally only knows existence results, more concrete by giving a detailed description in a special situation. [ABSTRACT FROM AUTHOR]

Introduction: We previously reported on the effectiveness of ureteroscopy-assisted retrograde nephrostomy during percutaneous nephrolithotomy and report two cases of lower calyx calculi in horseshoe kidney that were successfully treated with ureteroscopy-assisted retrograde nephrostomy. During the ureteroscopy-assisted retrograde nephrostomy procedure, a ureteroscope is advanced in the desired calyx and a Lawson retrograde nephrostomy puncture wire is inserted. The wire is advanced through the calyx to exit the skin. The wire is then used for the percutaneous dilation.Case Presentation: Case 1 was a 68-year-old man who was shown on radiography to have left lower calyx calculi (19 × 15mm, 7 × 5mm, and 7 × 3mm) in horseshoe kidney. Case 2 was a 36-year-old woman shown on radiography to have a left lower calyx calculus (10 × 8mm) in horseshoe kidney.Conclusions: Both patients were stone-free after ureteroscopy-assisted retrograde nephrostomy during percutaneous nephrolithotomy. Ureteroscopy-assisted retrograde nephrostomy is a promising procedure for safely and effectively treating lower calyx stones in horseshoe kidney. [ABSTRACT FROM AUTHOR]

We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x(t) = Ax(t) + f(t, x(t)), t ? R, where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem. [ABSTRACT FROM AUTHOR]

Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s ≥0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X, whose first and second generators are d and σ, respectively, and if d is also a σ-derivation then dn(ab) = (d + σ)n(a)*(d + σ)n(b) and αt,0(ab) = αt,1(a) * αt,1(b) for all a, b ∈ X. [ABSTRACT FROM AUTHOR]

Abstract: The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky–Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran–Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at given by the solution to Balitsky–Kovchegov equation, leads to the geometric scaling behavior. The McLerran–Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory. [Copyright &y& Elsevier]

The paper presents the calculus of the cut profile and the variation of this caused by the re-sharpening, that appears by a special profiled milling head construction, that uses cutting inserts. The advantage of the proposed milling head versus the classical concave profiled milling disk is evident, if considering the repartition of the cutting speed vector and the chip forming and exhausting conditions. The cutting insert's rake face is plain. Its relief face is a part of a common thorus realized by grinding. The insert occupies two distinct positions in the body of the tool: one for cutting and the other one for re-sharpening. Indexed positions are ensured through conical holes and corresponding slotted head sets. The re-sharpening can be done on the rake face or on the relief face. In both cases a minor profile error occurs but the profile is kept in the limits of the tolerance. This paper discusses the definition of the profile error and its dependence on the angular setting parameters and the number of the re-sharpening. The final conclusion is that the classical concave profiled milling disk can be replaced with the proposed variant. [ABSTRACT FROM AUTHOR]

Data envelopment analysis ( DEA) models assume real-valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision-making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming ( MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real-valued data. [ABSTRACT FROM AUTHOR]

For odd dimensional Poincaré-Einstein manifolds (Xn+1;g), we study the set of harmonic k-forms (for k < n/2 ) which are Cm (with m ∈ ℕ) on the conformal compactification X of X. This is infinite dimensional for small m but it becomes finite dimensional if m is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology Hk(X,∂X) and the kernel of the Branson-Gover [3] differential operators (Lk;Gk) on the conformal ifinity (∂X, [h0]). In a second time we relate the set of Cn-2k+1(Λk(X)) forms in the kernel of d + δg to the conformal harmonics on the boundary in the sense of [3], providing some sort of long exact sequence adapted to this setting. This study also provides another construction of Branson-Gover differential operators, including a parallel construction of the generalization of Q curvature for forms. [ABSTRACT FROM AUTHOR]

We show that if a polarized manifold admits an extarnal meiric then it is K-polystable relative to maximal torus of automoephisms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the infinitesimal deformations of the -color Lie superalgebra . By means of these deformations all filiform -color Lie superalgebras can be obtained. In particular, we give a method that will allow us to determine the dimension of the subspaces that are composed by linearly integrable deformations. [Copyright &y& Elsevier]

Given a formal symplectic groupoid G over a Poisson manifold ( M, π), we define a new object, an infinitesimal deformation of G, which can be thought of as a formal symplectic groupoid over the manifold M equipped with an infinitesimal deformation $${\pi_0 + \varepsilon \pi_1}$$ of the Poisson bivector field π. To any pair of natural star products $${(\ast,\tilde\ast)}$$ having the same formal symplectic groupoid G we relate an infinitesimal deformation of G. We call it the deformation groupoid of the pair $${(\ast,\tilde\ast)}$$ . To each star product with separation of variables $${\ast}$$ on a Kähler-Poisson manifold M we relate another star product with separation of variables $${\hat\ast}$$ on M. We build an algorithm for calculating the principal symbols of the components of the logarithm of the formal Berezin transform of a star product with separation of variables $${\ast}$$ . This algorithm is based upon the deformation groupoid of the pair $${(\ast,\hat\ast)}$$ . [ABSTRACT FROM AUTHOR]

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Abstract: A new method to construct C 1 triangular patches which satisfy the given boundary curves and cross-boundary slopes is presented. The Boolean sum of an approximation operator and an interpolation operator is employed to construct the triangular patch. The approximation operator is used to construct a polynomial patch of degree six. The polynomial of degree six affords more freedoms, which makes the approximation operator not only approximate the given boundary interpolation conditions but also have a better approximation precision in the interior of the triangle, so that the triangular patch has a better precision on both the boundary and the interior of the triangular domain. The interpolation operator is utilized to build an interpolation patch which satisfies the given boundary conditions. The Boolean sum of the approximation and interpolation patches forms the triangular patch. Comparison results of the new method with other three methods are given. [Copyright &y& Elsevier]

The locomotion of articulated mechanical systems is often complex and unintuitive, even when considered with the aid of reduction principles from geometric mechanics. In this paper, we present two tools for gaining insights into the underlying principles of locomotion: connection vector fields and connection height functions . Connection vector fields illustrate the geometric structure of the relationship between internal shape changes and the system body velocities they produce. Connection height functions measure the curvature of their respective vector fields and capture the net displacement over any cyclic shape change, or gait , allowing for the intuitive selection of gaits to produce desired displacements. Height function approaches have been previously attempted, but such techniques have been severely limited by their basis in a rotating body frame, and have only been useful for calculating planar rotations and infinitesimal translations. We circumvent this limitation by introducing a notion of optimal coordinates defining a body frame that rotates very little in response to shape changes, while still meeting the requirements of the geometric mechanics theory on which the vector fields and height functions are based. In these optimal coordinates, the height functions provide close approximations of the net displacement resulting from a broad selection of possible gaits. [ABSTRACT FROM AUTHOR]

Abstract: The goal of this paper is to present an explicit computation of the Birkhoff–Gustavson normal form in the , and resonances, by using the concept of Weyl quantization, especially when it is about the first terms. We use in particular the Weyl symbolic calculus and the abstract theorem of the quantum Birkhoff–Gustavson normal form in infinite dimension. [Copyright &y& Elsevier]

The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher-dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its nonlinear cohomology. [ABSTRACT FROM PUBLISHER]

We synthesize work of Koschorke on link maps and work of Johnson on the derivatives of the identity functor in homotopy theory. The result can be viewed in two ways: (1) as a generalization of Koschorke's ‘higher Hopf invariants’, which themselves can be viewed as a generalization of Milnor's invariants of link maps in Euclidean space; and (2) as a stable range description, in terms of bordism, of the cross-effects of the identity functor in homotopy theory evaluated at spheres. We also show how our generalized Milnor invariants fit into the framework of a multivariable manifold calculus of functors, as developed by the author and Volić, which is itself a generalization of the single variable version due to Weiss and Goodwillie. [ABSTRACT FROM PUBLISHER]

We define a torsion invariant T for every balanced sutured manifold (M, γ), and show that it agrees with the Euler characteristic of sutured Floer homology (SFH). The invariant T is easily computed using Fox calculus. With the help of T, we prove that if (M, γ) is complementary to a Seifert surface of an alternating knot, then SFH(M, γ) is either 0 or ℤ in every Spinc structure. The torsion invariant T can also be used to show that a sutured manifold is not disc decomposable, and to distinguish between Seifert surfaces.The support of SFH gives rise to a norm z on H2(M, ∂ M; ℝ). The invariant T gives a lower bound on the norm z, which in turn is at most the sutured Thurston norm xs. For closed 3-manifolds, it is well known that Floer homology determines the Thurston norm, but we show that z

Abstract: In this work, the option pricing Black–Scholes model with dividend yield is investigated via Lie symmetry analysis. As a result, the complete Lie symmetry group and infinitesimal generators of the one-dimensional Black–Scholes equation are derived. On the basis of these infinitesimal generators, the similarity variables and newly explicit solutions of the Black–Scholes equation are obtained by solving the corresponding characteristic equations. Finally, figures for an explicit solution with different dividend yields are presented to demonstrate the novel properties. [Copyright &y& Elsevier]

Let $ \mathbb{G}=\mathrm{Spin}[4n+1]$ and let $ G=\mathrm{Spin}(p,q)$ $ (p+q=4n+1)$ $ q \notin \left\{0,1\right\}$ has a nontrivial fundamental group and we denote the corresponding nonalgebraic double cover by $ \tilde{G}=\widetilde{\mathrm{Spin}}(p,q)$ at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality for the genuine characters of $ \tilde{G}$ [ABSTRACT FROM AUTHOR]

We consider the limiting distribution of $${U_NA_NU_N^*}$$ and B (and more general expressions), where A and B are N × N matrices with entries in a unital C*-algebra $${\mathcal B}$$ which have limiting $${\mathcal B}$$-valued distributions as N → ∞, and U is a N × N Haar distributed quantum unitary random matrix with entries independent from $${\mathcal B}$$. Under a boundedness assumption, we show that $${U_NA_NU_N^*}$$ and B are asymptotically free with amalgamation over $${\mathcal B}$$. Moreover, this also holds in the stronger infinitesimal sense of Belinschi-Shlyakhtenko. We provide an example which demonstrates that this result may fail for classical Haar unitary random matrices when the algebra $${\mathcal B}$$ is infinite-dimensional. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes a particularly simple form of the exact solutions for two-dimensional electromagnetic wave diffraction by a slot in the plane perfectly conducting screen with infinitesimal thickness, and by a complementary strip. Following the mode-matching technique, the problem is formulated in terms of dual integral equations in Fourier amplitudes of diffraction fields, which are solved by infinite discrete Fourier series in slot (strip) modes. For the coefficients of these series (or mode amplitudes), the dual equations yield linear systems of algebraic equations. [ABSTRACT FROM AUTHOR]

We revisit the gauging of rigid symmetries in two-dimensional bosonic sigma models with a Wess-Zumino term in the action. Such a term is related to a background closed 3-form H on the target space. More exactly, the sigma-model Feynman amplitudes of classical fields are associated to a bundle gerbe with connection of curvature H over the target space. Under conditions that were unraveled more than twenty years ago, the classical amplitudes may be coupled to the topologically trivial gauge fields of the symmetry group in a way which assures infinitesimal gauge invariance. We show that the resulting gauged Wess-Zumino amplitudes may, nevertheless, exhibit global gauge anomalies that we fully classify. The general results are illustrated on the example of the WZW and the coset models of conformal field theory. The latter are shown to be inconsistent in the presence of global anomalies. We introduce a notion of equivariant gerbes that allow an anomaly-free coupling of the Wess-Zumino amplitudes to all gauge fields, including the ones in non-trivial principal bundles. Obstructions to the existence of equivariant gerbes and their classification are discussed. The choice of different equivariant structures on the same bundle gerbe gives rise to a new type of discrete-torsion ambiguities in the gauged amplitudes. An explicit construction of gerbes equivariant with respect to the adjoint symmetries over compact simply connected simple Lie groups is given. [ABSTRACT FROM AUTHOR]

We obtain a description of the maximum and minimum values of the remainder in the problem of the distribution of fractional parts. The exact maximum and minimum values of the remainder are calculated; they are independent of the length of the bounded remainder interval. It is shown that these values can be computed in O( m) operations. The remainder is described as a function of the argument α. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the challenging problem of encoding the common sense knowledge involved in the manipulation of spatial objects from a reasoning about actions and change perspective. In particular, we propose a formal solution to a puzzle composed of non-trivial objects (such as holes and strings) assuming a version of the Situation Calculus written over first-order Equilibrium Logic, whose models generalise the stable model semantics. [ABSTRACT FROM AUTHOR]

Abstract: Logical filtering is the process of updating a belief state (set of possible world states) after a sequence of executed actions and perceived observations. In general, it is intractable in dynamic domains that include many objects and relationships. Still, potential applications for such domains (e.g., semantic web, autonomous agents, and partial-knowledge games) encourage research beyond intractability results. In this paper we present polynomial-time algorithms for filtering belief states that are encoded as First-Order Logic (FOL) formulas. Our algorithms are exact in many cases of interest. They accept belief states in FOL without functions, permitting arbitrary arity for predicates, infinite universes of elements, and equality. They enable natural representation with explicit references to unidentified objects and partially known relationships, still maintaining tractable computation. Previous results focus on more general cases that are intractable or permit only imprecise filtering. Our algorithms guarantee that belief-state representation remains compact for STRIPS actions (among others) with unbounded-size domains. This guarantees tractable exact filtering indefinitely for those domains. The rest of our results apply to expressive modeling languages, such as partial databases and belief revision in FOL. [ABSTRACT FROM AUTHOR]

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevskiĭ 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron is not stationary under the flex. [ABSTRACT FROM AUTHOR]

This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this work is to generalize nilpotent Lie superalgebras of a very important type, i.e. filiform Lie superalgebras, obtaining the notion of filiform color Lie superalgebras. We have proved the existence of an adapted basis for any -grading of the filiform color superalgebras. Also we have proved that in order to obtain the whole class of filiform -color Lie superalgebras it is only necessary to determine the infinitesimal deformations of the associated model color superalgebra. [ABSTRACT FROM AUTHOR]