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An analytical approach about the general type of step-index optical fiber modes and their variations is presented in this paper. The theoretical model is solved through our analytical method. With the boundary conditions, a composite equation set is established and solved. The precise results of all modes are achieved with a high-precision numerical solution. The modal characteristic contains the distributions of electromagnetic fields, the effective refractive index, and its tendencies. The modal sensitivity is based on the former and the partial derivative of the effective refractive index (neff/ni and neff/ri). The derivative rule of implicit functions and determinant function allows our method to analyze the sensitivity of modes. Furthermore, four qualitative deductions are derived during the process, including the qualitative analysis of modes and their constraints, supporting previous experiments. Our work is beneficial for exploiting new fiber and researching relative fiber sensors.

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over $S^1$.

We develop the Gompf fiber connected sum operation for symplectic orbifolds. We use it to construct a symplectic 4-orbifold with b 1 = 0 {b_{1}=0} and containing symplectic surfaces of genus 1 and 2 that are disjoint and span the rational homology. This is used in turn to construct a K-contact Smale–Barden manifold with specified 2-homology that satisfies the known topological constraints with sharper estimates than the examples constructed previously. The manifold can be chosen spin or non-spin.

We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one defined by Lusztig in Lfromto, (2011) and that the Kazhdan–Lusztig map in Kazhdan and Lusztig, (1998) is a section of our map. This settles several conjectures in the literature. For classical groups, we prove more refined results by introducing and studying the “skeleta” of affine Springer fibers.

Let $X$ be a bundle over $S^1$ with fiber a 3--manifold $M$ and with monodromy $\varphi$. Gay and Kirby showed that if $\varphi$ fixes a genus $g$ Heegaard splitting of $M$ then $X$ has a genus $6g+1$ trisection. Genus $3g+1$ trisections have been found in certain special cases, such as the case where $\varphi$ is trivial, and it is known that trisections of genus lower than $3g+1$ cannot exist in general. We generalize these results to prove that there exists a trisection of genus $3g+1$ whenever $\varphi$ fixes a genus $g$ Heegaard surface of $M$. This means that $\varphi$ can be nontrivial, and can preserve or switch the two handlebodies of the Heegaard splitting. We additionally describe an algorithm to draw a diagram for such a trisection given a Heegaard diagram for $M$ and a description of $\varphi$.

We explain an algorithm to calculate Arthur’s weighted orbital integral in terms of the number of rational points on the fundamental domain of the associated affine Springer fiber. The strategy is to count the number of rational points of the truncated affine Springer fibers in two ways: by the Arthur–Kottwitz reduction and by the Harder–Narasimhan reduction. A comparison of results obtained from these two approaches gives recurrence relations between the number of rational points on the fundamental domains of the affine Springer fibers and Arthur’s weighted orbital integrals. As an example, we calculate Arthur’s weighted orbital integrals for the groups ${\textrm {GL}}_{2}$ and ${\textrm {GL}}_{3}$ .

We consider Hessenberg varieties in the flag variety of $GL_n(\mathbb{C})$ with the property that the corresponding Hessenberg function defines an ad-nilpotent ideal. Each such Hessenberg variety is contained in a Springer fiber. We extend a theorem of Tymoczko to this setting, showing that these varieties have an affine paving obtained by intersecting with Schubert cells. Our method of proof constructs an an affine paving for each Springer fiber that restricts to an affine paving of the Hessenberg variety. We use the combinatorial properties of this paving to prove that Hessenberg varieties of this kind are connected., Comment: 21 pages

To each variety $X$ and a nonnegative integer $m$, there is a space $X_m$ over $X$, called the jet scheme of $X$ of order $m$, parametrizing $m$-th jets on $X$. Its fiber over a singular point of $X$ is called a singular fiber. For a surface with a rational double point, Mourtada gave a one-to-one correspondence between the irreducible components of the singular fiber of $X_m$ and the exceptional curves of the minimal resolution of $X$ for $m \gg 0$. In this paper, for a surface $X$ over complex number with a singularity of $A_n$ or $D_4$-type, we study the intersections of irreducible components of the singular fiber and construct a graph using this information. The vertices of the graph correspond to irreducible components of the singular fiber and two vertices are connected when the intersection of the corresponding components is maximal for the inclusion relation. In the case of $A_n$ or $D_4$-type singularity, we show that this graph is isomorphic to the resolution graph for $m \gg 0$., 18 pages

In this paper, a new consistent analytical model is proposed for second-order direct analysis of steel structures with tapered members allowing for both symmetric and asymmetric variations. The proposed model is implemented in a flexibility-based beam-column element with considering initial geometrical imperfections at the element level. To account for the influence of varied tapering ratios on the member behavior, a new initial geometrical imperfection pattern is introduced for both prismatic and non-prismatic members using common section shapes such as I-shape, Tee-shape, circular and rectangular hollow sections. Note that the conventional bow imperfection pattern that is widely accepted for prismatic members may lead to unsafe design when it is adopted for the tapered members. Furthermore, residual stress is explicitly considered through a fiber section approach in the proposed beam-column element. Consequently, the traditional effective length method is no longer required, as both geometrical imperfections and residual stress have been taken into account. The progressive yielding behavior of tapered members is also considered through the fiber section with nonlinear stress–strain relationships. Thus, a comprehensive second-order direct analysis method is proposed for safer and more economical design of tapered structures without the assumption of the effective length factor for a stability check. Several numerical examples are employed to verify the accuracy and practicability of the proposed model.

Equivalent-graded-index photonic-crystal fiber (EGI-PCF) is a modified photonic-crystal fiber (PCF) where the cladding is not required to be periodic. A radial gradient of the equivalent refractive index distribution provides extra freedom to efficiently tailor the dispersion of EGI-PCF. However, such additional complexity makes the manual fiber design much more challenging where the time consumption becomes too much to be afforded eventually. In this paper, we for the first time propose the method of computer-aided inverse fiber design (CAFD) based on empirical dispersion formula to circumvent this hurdle. We apply the differential evolution (DE) genetic algorithm to seek for the optimized EGI-PCF design with a target of specific dispersion profile. In the dispersion oriented EGI-PCF design, the use of empirical formula instead of numerical simulation (e.g., finite-element method) is proved to greatly reduce the run-time of CAFD and simplifies the fitness function evaluation as much as possible. We adopt our method and demonstrate a design of EGI-PCF with a near-zero ultra-flattened dispersion in the whole S+C+L band, which merely costs a few seconds of a laptop to return an optimized fiber design. Thus improvement of efficiency is about three orders of magnitude faster than any previous CAFD attempts as far as we learn. In the end, we use our method to explore an EGI-PCF design with a unique dispersion profile of all-normal dispersion-decreasing along the fiber length centered around 1 μm that plays a key role for the self-similar pulse evolution in a fiber laser/amplifier.

Anisotropic fiber-reinforced composites are used in lightweight construction, which is of great industrial relevance. During mold filling of fiber suspensions, the microstructural evolution of the local fiber arrangement and orientation distribution is determined by the local velocity gradient. Based on the Folgar–Tucker equation, which describes the evolution of the second-order fiber orientation tensor in terms of the velocity gradient, the present study addresses selected states of deformation rates that can locally occur in complex flow fields. For such homogeneous flows, exact solutions for the asymptotic fiber orientation states are derived and discussed based on the quadratic closure. In contrast to the existing literature, the derived exact solutions take into account the fiber-fiber interaction. The analysis of the asymptotic solutions relying upon the common quadratic closure shows disadvantages with respect to the predicted material symmetry, namely, the anisotropy is overestimated for strong fiber-fiber interaction. This motivates us to suggest a novel normalized fully symmetric quadratic closure. Two versions of this new closure are derived regarding the prediction of anisotropic properties and the fiber orientation evolution. The fiber orientation states determined with the new closure approach show an improved prediction of anisotropy in both effective viscous and elastic composite behaviors. In addition, the symmetrized quadratic closure has a simple structure that reduces the effort in numerical implementation compared to more elaborated closure schemes.

We prove a representation stability result for the Milnor fiber associated to the pure braid group. Our result connects previous work of Simona Settepenella to representation stability in the sense of Church--Ellenberg--Farb, answering a question of Graham Denham. We also use our result to compute the stable integral homology of the Milnor fiber.

Moduli spaces of bounded local G-shtukas are a group-theoretic generalisation of the function field analogue of Rapoport and Zink’s moduli spaces of p-divisible groups. In this article we generalise some very prominent concepts in the theory of Rapoport-Zink spaces to our setting. More precisely, we define period spaces, as well as the period map from a moduli space of bounded local G-shtukas to the corresponding period space, and we determine the image of the period map. Furthermore, we define a tower of coverings of the generic fibre of the moduli space, which is equipped with a Hecke action and an action of a suitable automorphism group. Finally, we consider the $\ell $ -adic cohomology of these towers.Les espaces de modules de G-chtoucas locaux bornés sont une généralisation des espaces de modules de groupes p-divisibles de Rapoport-Zink, au cas d’un corps de fonctions local, pour des groupes plus généraux et des copoids pas nécessairement minuscules. Dans cet article nous définissons les espaces de périodes et l’application de périodes associés à un tel espace, et nous calculons son image. Nous étudions la tour au-dessus de la fibre générique de l’espace de modules, équipée d’une action de Hecke ainsi que d’une action d’un groupe d’automorphismes. Enfin, nous définissons la cohomologie $\ell $ -adique de ces tours.

We describe the topology of the local Milnor fiber of a function f defined on a 3-dimensional subanalytic subset $$W \subset {\mathbb {R}}^3$$ , in terms of the embedded topological type of its link $$K_f$$ . Precisely, we prove that the interior of the local Milnor fiber of $$\Vert f\Vert $$ is homeomorphic to the complement of $$K_f$$ in the corresponding sphere, extending a result due to Milnor to non-analytic situations. We also prove that the topology of the fiber does not change if we use a suitable fundamental system of neighborhoods instead of balls, extending to the real setting a classical result due to Le and Teissier for complex functions.

In this paper, warped product mixed generalized quasi-Einstein manifolds MG(QE) $$_{n}$$ are studied. It is shown that a Ricci recurrent MG(QE) $$_{n}$$ manifold is a product manifold whose factors are Ricci recurrent. Sufficient conditions for a MG(QE) $$_{n}$$ to be a G(QE) $$_{n}$$ are derived. Then, we classify three types of warped product MG(QE) $$_{n}$$ . For example, it is proved that the fiber manifold is Einstein in the first type, (QE) $$_{n}$$ in the second type and MG(QE) $$_{n}$$ in the third type.

We study the Picard–Lefschetz formula for Siegel modular threefolds of paramodular level and prove the weight-monodromy conjecture for its middle degree inner cohomology. We give some applications to the Langlands programme: using Rapoport-Zink uniformisation of the supersingular locus of the special fiber, we construct a geometric Jacquet–Langlands correspondence between $${\text {GSp}}_4$$ GSp 4 and a definite inner form, proving a conjecture of Ibukiyama. We also prove an integral version of the weight-monodromy conjecture and use it to deduce a level lowering result for cohomological cuspidal automorphic representations of $${\text {GSp}}_4$$ GSp 4 .

We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and total space are smoothable as manifolds. These non-smoothable topological families provide new examples of 4-manifolds $M$ for which the inclusion maps $\operatorname{Diff}(M) \hookrightarrow \operatorname{Homeo}(M)$ are not weak homotopy equivalences. We shall also give a new series of non-smoothable topological actions on some spin 4-manifolds., 40 pages, to appear in Compositio Mathematica

Consider a very general abelian variety $A$ of dimension at least $3$ and an integer $0, Comment: 9 pages

We present a relation between the classical Chow group of relative $0$-cycles on a regular scheme $\mathcal{X}$, projective and flat over an excellent Henselian discrete valuation ring, and the Levine-Weibel Chow group of 0-cycles on the special fiber. We show that these two Chow groups are isomorphic with finite coefficients under extra assumptions. This generalizes a result of Esnault, Kerz and Wittenberg., Comment: 21 pages. Final version. To appear in Annali della Scuola Normale Superiore di Pisa

Consider a family of Fano varieties $$\pi :X \rightarrow B\ni o$$ over a curve germ with a smooth total space X. Assume that the generic fiber is smooth and the special fiber $$F=\pi ^{-1}(o)$$ has simple normal crossings. Then F is called a semistable degeneration of Fano varieties. We show that the dual complex of F is a simplex of dimension $$\hbox {\,\char 054\,}\mathrm {dim}\, F$$ . Simplices of any admissible dimension can be realized for any dimension of the fiber. Using this result and the Minimal Model Program in dimension 3 we reproduce the classification of the semistable degenerations of del Pezzo surfaces obtained by Fujita. We also show that the maximal degeneration is unique and has trivial monodromy in dimension $$\hbox {\,\char 054\,}\,3$$ .

In the present paper, we study the (twisted) 3-canonical map of varieties of Albanese fiber dimension one. Based on a theorem about the regularity of direct image of canonical sheaves, we prove that the 3-canonical map is generically birational when the genus of a general fiber of the Albanese map is 2., Comment: 14 pages

Let [Formula: see text] be a Noetherian local ring with maximal ideal [Formula: see text], [Formula: see text] an ideal of [Formula: see text], [Formula: see text] an [Formula: see text]-primary ideal of [Formula: see text], [Formula: see text] a finitely generated [Formula: see text]-module, [Formula: see text] a finitely generated standard graded algebra over [Formula: see text] and [Formula: see text] a finitely generated graded [Formula: see text]-module. We characterize the multiplicity and the Cohen–Macaulayness of the fiber cone [Formula: see text]. As an application, we obtain some results on the multiplicity and the Cohen–Macaulayness of the fiber cone[Formula: see text].

We discuss $\mathrm{L}^p$ fiber spaces which appear, e.g., as extrapolation spaces of unbounded multiplication operators which in turn are motivated, for instance, by non-autonomous evolution equations., Comment: 8 pages

In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I × ρ M f n whose fiber M has f -parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products.

For any two integers $k,n$, $2\leq k\leq n$, let $f:(\mathbb{C}^*)^n\rightarrow\mathbb{C}^k$ be a generic polynomial map with given Newton polytopes. It is known that points, whose fiber under $f$ has codimension one, form a finite set $C_1(f)$ in $\mathbb{C}^k$. For maps $f$ above, we show that $C_1(f)$ is empty if $k\geq 3$, we classify all Newton polytopes contributing to $C_1(f)\neq \emptyset$ for $k=2$, and we compute $|C_1(f)|$., Comment: Final version, Minor corrections, 6 pages, to appear in Colloquium Mathematicum

Improving the efficiency of the process of separating fiber from cotton seeds by improving the working chamber of the gin is one of the important issues. The main way to increase the efficiency of sawn gin is to increase the fiber content in the mass of seeds in the working chamber with a uniform decrease in its density. This can be achieved by using grates with a concave working surface, which serves to move the seeds away from the rotating saws and accelerate the release of bare seeds from the working chamber. The article discusses the movement of seeds on the concave surface of the grate and determines the rational parameters of their working part. The article explores the proposed grate model, consisting of four geometric shapes, provides an analytical analysis of the geometric types. The dependence of the location of the last rectilinear part of the general contour on the shape of its convexity and concavity is determined. Cotton seeds move along the contour in the form of a stream. We assume that the thickness of the flow along the contour is constant and equal. We compose a unique equation of the flow in each section of the circuit. To determine the state of the flow, we denote its velocity, density and pressure in each section, respectively. Let us determine the flow motion along the contour with respect to the arc.

We introduce tame sc-Fredholm sections and slices of sc-Fredholm sections. A slice is a notion of subpolyfold that is compatible with the sc-Fredholm section and has finite locally constant codimension. We prove that the subspace of a tame polyfold that satisfies a transverse sc-smooth constraint in a finite dimensional smooth manifold is a slice of any tame sc-Fredholm section compatible with the constraint. Moreover, we prove that a sc-Fredholm section restricted to a slice is a tame sc-Fredholm section with a drop in Fredholm index given by the codimension of the slice. As a corollary, we obtain fiber products of tame sc-Fredholm sections. We describe applications to Gromov-Witten invariants, constructing the Piunikhin-Salamon-Schwarz maps for general closed symplectic manifolds, and avoiding sphere bubbles in moduli spaces of expected dimension $0$ and $1$., To appear in Journal of Symplectic Geometry. 97 pages. Revised based on referee suggestions. Numbering of results has changed

We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma}$, we show that it has a continuous invariant family of $\gamma$-H\"older Riemannian metrics on $M$. We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle., Comment: 24 pages

We determine the structure of the fibered biset functor sending a finite group $G$ to the complex vector space of complex valued class functions of $G$. Previously, it is studied as a biset functor by Bouc and as a $\mathbb C^\times$-fibered biset functor by Boltje and the second author. In this paper, we complete the study by considering the other choices of the fiber group. As a corollary, we obtain a (previously known) set of composition factors of the biset functor of $p$-permutation modules., Comment: 27 pages

It is shown that Liouville foliations of the family of non-Euclidean analogs of Kovalevskaya integrable system on a pencil of Lie algebras have both compact and noncompact fibers. There exists a bifurcation of their compact common level surface into a noncompact one that has a noncompact singular fiber. In particular, this is true for the non-Euclidean $$e(2,1)$$ -analog of the Kovalevskaya case of rigid body dynamics. In the case of nonzero area integral, an effective criterion for existence of a noncompact connected component of the common level surface of first integrals and Casimir functions is proved.

Purpose The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar–Tucker equation for the fiber orientation behavior. Design/methodology/approach First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar–Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability. Findings The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases. Originality/value The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.

We investigate the geometry of complete spacelike hypersurfaces (immersed) in a generalized Robertson-Walker spacetime $$-I\times _fM^{n}$$ . Under suitable constraints on the sectional curvature of the Riemannian fiber $$M^n$$ , on the warping function f and on the future mean curvature (that is, the mean curvature function with respect to the future-pointing Gauss map of the spacelike hypersurface), we are able to prove that such a spacelike hypersurface must be a slice $$\{t\}\times M^{n}$$ of the ambient spacetime. Nonexistence and Calabi–Bernstein type results concerning entire spacelike graphs constructed over the Riemannian fiber $$M^n$$ are also obtained, as well as applications to the Einstein–de Sitter and steady state type spacetimes are given. Our approach is based on the so-called Omori–Yau’s generalized maximum principle and on certain integrability properties due to Yau.

We put forward in this paper a uniform narrative that weaves together several variants of Hrushovski-Kazhdan style integral, and describe how it can facilitate the understanding of the Denef-Loeser motivic Milnor fiber and closely related objects. Our study focuses on the so-called "nonarchimedean Milnor fiber" that was introduced by Hrushovski and Loeser, and our thesis is that it is a richer embodiment of the underlying philosophy of the Milnor construction. The said narrative is first developed in the more natural complex environment, and is then extended to the real one via descent. In the process of doing so, we are able to provide more illuminating new proofs, free of resolution of singularities, of a few pivotal results in the literature, both complex and real. To begin with, the real motivic zeta function is shown to be rational, which yields the real motivic Milnor fiber; this is an analogue of the Hrushovski-Loeser construction. We also establish, in a much more intuitive manner, a new Thom-Sebastiani formula, which can be specialized to the one given by Guibert, Loeser, and Merle. Finally, applying $T$-convex integration after descent, matching the Euler Characteristics of the topological Milnor fiber and the motivic Milnor fiber becomes a matter of simple computation, which is not only free of resolution of singularities as in the Hrushovski-Loeser proof, but is also free of other sophisticated algebro-geometric machineries.

This study evaluated the fibre morphology of Musa balbisiana leaf, stalk and stem portions for pulp and paper production. Samples of Musa balbisiana portions were prepared and macerated in equal volume of glacial acetic acid and hydrogen peroxide in ratio 1:1. Twenty cellulose fibres from each portion were randomly selected using Reichert visopan microscope to determine the physical fibre morphology while the derived fibre indices were calculated. Data collected were subjected to one way Analysis of Variance (ANOVA). Follow up tests carried out using Duncan Multiple Range Test (DMRT). Results showed that means of fibre length, fibre diameter, cell wall thickness and lumen width ranged between 1.35 and 2.46 mm, 16.46 and 33.34 µm, 7.58 and 24.99 µm, and 3.54 and 3.56 µm, respectively. The mean values of fibre length of Musa balbisiana leaf and stalk were not significant but were significantly different from the mean values of the stem at p

Jute fiber has a great role in Indian economy. Since, jute fiber quality varies one place to another owing to various reasons, it becomes imperative to go for classification and gradation of jute f...

We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber extend to all fibers. We then show that quantized coordinate rings of flag varieties and Schubert varieties can be filtered so that the associated graded rings are twisted semigroup rings in the sense of [RZ12]. This is a noncommutative version of the result due to Caldero [C02] stating that flag and Schubert varieties degenerate into toric varieties, and implies that quantized coordinate rings of flag and Schubert varieties are AS-Cohen–Macaulay. Fil: Rigal, L.. Universite de Paris 13-Nord; Francia Fil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina

In this article, we describe the underlying reduced scheme of a quaternionic unitary Rapoport–Zink space with Iwahori level structure. In a previous work, we have studied the quaternionic unitary Rapoport–Zink space with a special maximal parahoric level structure. We will describe the morphism between these two Rapoport–Zink spaces and the fibers of this morphism. As an application of this result, we describe the quaternionic unitary Rapoport–Zink space with any parahoric level structure.

We give a streamlined proof of A(1)-representability for G-torsors under "isotropic" reductive groups, extending previous results in this sequence of papers to finite fields. We then analyze a collection of group homomorphisms that yield fiber sequences in A(1)-homotopy theory, and identify the final examples of motivic spheres that arise as homogeneous spaces for reductive groups.

For a family of varieties, we prove that the alternating sum of the traces of “local” monodromy acting on the $$\ell $$ -adic etale cohomology groups of the generic fiber is an integer that is independent of $$\ell $$ . In the course of the proof, we also establish a result on fixed points.

For a map $$f:X\rightarrow Y$$ f : X → Y , there is the relative model $$M(Y)=(\Lambda V,d)\rightarrow (\Lambda V\otimes \Lambda W,D)\simeq M(X)$$ M ( Y ) = ( Λ V , d ) → ( Λ V ⊗ Λ W , D ) ≃ M ( X ) by Sullivan model theory (Félix et al., Rational homotopy theory, graduate texts in mathematics, Springer, Berlin, 2007). Let $$\mathrm{Baut}_1X$$ Baut 1 X be the Dold–Lashof classifying space of orientable fibrations with fiber X (Dold and Lashof, Ill J Math 3:285–305, 1959]). Its DGL (differential graded Lie algebra)-model is given by the derivations $$\mathrm{Der}M(X)$$ Der M ( X ) of the Sullivan minimal model M(X) of X. Then we consider the condition that the restriction $$b_f:\mathrm{Der} (\Lambda V\otimes \Lambda W,D)\rightarrow \mathrm{Der}(\Lambda V,d) $$ b f : Der ( Λ V ⊗ Λ W , D ) → Der ( Λ V , d ) is a DGL-map and the related topics.

Recently, Skabelund defined new maximal curves which are cyclic extensions of the Suzuki and Ree curves. Previously, the now well-known GK curves were found as cyclic extensions of the Hermitian curve. In this paper, we consider locally recoverable codes constructed from these new curves, complementing that done for the GK curve. Locally recoverable codes allow for the recovery of a single symbol by accessing only a few others which form what is known as a recovery set. If every symbol has at least two disjoint recovery sets, the code is said to have availability. Three constructions are described, as each best fits a particular situation. The first employs the original construction of locally recoverable codes from curves by Tamo and Barg. The second yields codes with availability by appealing to the use of fiber products as described by Haymaker, Malmskog, and Matthews, while the third accomplishes availability by taking products of codes themselves. We see that cyclic extensions of the Deligne–Lusztig curves provide codes with smaller locality than those typically found in the literature.

In the present study, the aeroelastic energy response of a twin-engine composite wing system is optimized based on sequential quadratic programming (SQP) method. The variable stiffness is acquired by constructing laminates of thin wall beam (TWB) with curvilinear fibers having prescribed paths. In order to account the effect of spanwise locations and mass of the engines on the aeroelastic characteristics of TWB, the novel governing equations of motion are obtained using Hamilton's variational principle. The paper aims to exploit desirable fiber paths with improved aeroelastic properties for different twin-engine wing configuration. Ritz based solution methodology is employed to solve the equations with coupled incompressible unsteady aerodynamic model based on Wagner’s function. A novel optimization strategy based on the total energy of the aeroelastic system is introduced. The proposed total energy, as a cost function, is minimized in terms of four optimization variables of two engine’s locations and wing structure curvilinear fiber angle with two design parameters. The total energy is obtained by integrating responses of kinetic and potential energy in a specific time interval. The minimum total energy is an indication of ideal optimization variables which leads to the optimum flutter performance. Numerical results demonstrate the effectiveness of the optimization variables on the total energy of the aeroelastic system and determine the optimal values of introduced variables in case of minimum total energy and improved aeroelastic characteristics.

For C r ( r > 1 ) random dynamical systems F on a compact smooth Riemannian manifold M, the fiber topological entropy is bounded above by an integral formula. Particularly, for the C ∞ random dynamical systems, the integral formula coincides with the fiber topological entropy.

In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of [GK93] and the Siegel series have the same inherent structures, beyond matching values. As an application, we will prove a new identity between the intersection number of two modular correspondences over Fp and the sum of the Fourier coefficients of the Siegel-Eisenstein series for Sp_4 of weight 2, which is independent of p (> 2). In addition, we will explain a description of the local intersection multiplicities of the special cycles over F_p on the supersingular locus of the `special fiber' of the Shimura varieties for GSpin(n; 2), n, 52 pages

In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit into this context (as for example banachanalytic spaces, Kahler spaces etc.)

We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci., Comment: Final version, several typos fixed. Any comments are welcome!

In this article we investigate mixed polynomials and present conditions that can be applied on a specific class of polynomials in order to prove the existence of the Milnor Fibration, Milnor–LeFibration and the equivalence between them. We prove for this class the of functions that the Milnor–Le fiber on a regular value is homeomorphic to the Milnor–Le fiber on a critical value. We develop a criterion to verify the transversality property and apply it to a special case of the class of mixed polynomial.

Let [math] be a compact orientable aspherical [math] –manifold. We show that if the profinite completion of [math] is isomorphic to the profinite completion of a free-by-cyclic group or to the profinite completion of a surface-by-cyclic group, then [math] fibers over the circle with compact fiber.