Asan Application Research Articles

Derived $F$-zips

We define derived versions of $F$-zips and associate a derived $F$-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived $F$-zips and certain substacks. We make a connection to the classical theory and look at problems that arise when trying to generalize the theory to derived $G$-zips and derived $F$-zips associated to lci morphisms. As an application, we look at Enriques-surfaces and analyze the geometry of the moduli stack of Enriques-surfaces via the associated derived $F$-zips. As there are Enriques-surfaces in characteristic $2$ with non-degenerate Hodge-de Rham spectral sequence, this gives a new approach, which could previously not be obtained by the classical theory of $F$-zips.

Generalized Rayleigh-Quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of Simple Eigenvalues of Compact Operators

In an earlier paper, the author derived generalized Rayleigh-quotient formulas for the real parts, imaginary parts, and moduli of the eigenvalues of diagonalizable matrices. More precisely, max-, min-max-, min-, and max-min-formulas were obtained. In this paper, we extend these results to the eigenvalues of linear nonsymmetric compact operators with simple eigenvalues in a Hilbert space. As an application, a new formula for the spectral radius is derived. An example arising from a boundary value problem in Mathematical Physics illustrates the general results, and numerical computations underpin the theoretical findings. In addition, the Euler column is treated from the area of Elastomechanics, which is complemented by references to other examples from this area.

Existence and uniqueness solution for integral boundary value problem of fractional differential equation

In this work, we will study the existence and uniqueness results of a class of nonlinear fractional differential equations with integral boundary value conditions. By using Leray-Schauder nonlinear alternative and the Banach contraction mapping principle. As an application, an example is given to prove our conclusions.

Coincidence Point Results in Ordered Metric Spaces and its Application

In this paper, we establish some coincidence point theorems of nonlinear rational contractions in a complete partially ordered metric space. Some consequences of the results are presented in terms of integral contractions and few examples are illustrated to support the results. As an application, we proved the existence of a unique solution to an integral equation.

Improvement of the designmethodof thermal networks: serialconnection of heat exchangers

The mathematical model of the system is considered consisting of a series connection of three heating devices. A system of equations based on the energy conservation law is constructed, which turns out to be incomplete. It is shown that, given the known requirements for the system, expressed only in the efficiency of the system, the formalization of design often becomes insoluble.The system of equations is supplemented with expressions in accordance with the hypothesis of the proportionality of the amount of energy in an element and is presented in matrix form. The design task is reduced to determining the elements of the matrix by the value of the determinants. Analysis of the mathematical model made it possible to obtain an expression for the efficiency of the system as a function of energy exchange in its elements.This made it possible to obtain solutions for flows and their relationships in the elements of the system. In addition, the efficiency of inter-network and intra-network energy exchange has been determined, which satisfy the principles of equilibrium and minimum uncertainty in the values of the average parameters of the system. Asan application, one of the main parameters, NTU,is considered, which determines the area of heat exchange with the external environment and the mass and dimensional characteristics of the heat exchange system.Models of direct and opposite switching on of flows with variations of flows and the value of the surface of devices when meeting the requirements for the efficiencyof the system are considered. The results of comparing the design process with the iterative calculation method are presented and the advantages of the proposed approach are shown.

Towards a Digital Twin Enabled Multifidelity Framework for Small Satellites

In this work, a multi-fidelity framework for the simulation ofsmall satellites is investigated. Taking into account the conceptof digital twin, our work focuses on handling a constantstream of live data. Towards this end, current multi-fidelitymodelling methods and low fidelity surrogate models for timeseries were surveyed. A multi-fidelity approach is used tocombine a low fidelity surrogate model with a high fidelitymodel. As a high fidelity model, a previously investigatedfinite element model is assumed. As a low fidelity model,auto-regressive and recurrent neural network-based modelsare investigated. Through cokriging, the low fidelity data iscorrected by the high fidelity data through a comprehensivecorrection, where the parameters are given through Gaussianprocesses in order to perform uncertainty quantification. Asan application, the thermal simulation of a small satellite, andthe use of this framework in conjunction with sparse telemetrydata is proposed. This online, statistical approach aims toprovide a tool for performing fault detection.

The Relation “Commutator Equals Function” in Banach Algebras

The relation $xy-yx=h(y)$, where $h$ is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach a rigorous meaning to the right-hand side of this equality, we assume that $x$ and $y$ are elements of a Banach algebra (or of an Arens--Michael algebra). We prove that the universal algebra generated by a commutation relation of this kind can be represented explicitly as an analytic Ore extension. An analysis of the structure of the algebra shows that the set of holomorphic functions of $y$ degenerates, but at each zero of $h$, some local algebra of power series remains. Moreover, this local algebra depends only on the order of the zero. As an application, we prove a result about closed subalgebras of holomorphically finitely generated algebras.

The Pb-cone metric spaces over Banach algebra with applications

The aim of the article is to establish the structure of partial cone b-metric spaces over Banach algebras. Topological and structural properties are investigated of the new spaces. We also define generalized Lipschitz mappings and give their application in fixed point theory. The results presented in this paper substantially extend and strengthen the results of the literature. Few examples are provided to support our conclusions and as an application we establish the existence and uniqueness of a solution to a class of system of nonlinear integral equations.

Optimal Bayesian Mechanisms Without Monetary Transfers: A Solution to the Two-Person Implementation Problem

We study the relationship between two-agent implementation problems and the notion of interim efficiency due to Holmstrom and Myerson (1983) in Bayesian environments with private values and independent types. We present a general property, Bayesian efficiency, and show that it is sufficient for implementation of social choice functions. We also show that this condition is sufficient for implementation of social choice sets under a weak domain restriction - in particular, no economic condition is required. As an application, we show that the generalized two-person Nash bargaining solution, due to Myerson (1984), is Bayesian efficient.

Euler characteristics and $q$-difference equations

This paper is concerned with linear q-difference equations. Our main result is an explicit formula for the Euler characteristic of the sheaf of analytic solutions attached to any linear algebraic q-difference equation. This formula involves certain invariants attached to the so-called intermediate singularities. As an application, we interpret the index of rigidity recently introduced by Sakai and Yamaguchi in cohomological terms.

Relaciones entre teoría y práctica en la formación inicial. Percepciones de formadores y estudiantes del Grado de Maestro en Educación primaria

<p> </p><p> </p><p>El propósito básico de este artículo es el de explorar las relaciones teoría y práctica en la formación inicial del Grado de Maestro en Educación primaria de la Universidad de Santiago de Compostela (USC). El trabajo forma parte de un proyecto de investigación más amplio que se propuso identificar, analizar e interpretar las percepciones de futuros profesores y sus formadores sobre los conocimientos que están construyendo en el desarrollo del Plan de estudios del Grado de Maestro en Educación Primaria y la contribución de estos a configurar una identidad profesional determinada. Con un enfoque metodológico cualitativo se utilizó análisis documental, relatos, grupos de discusión y entrevistas a profesorado, coordinadores de titulación, decanos, estudiantes y tutores/as de Practicum durante el periodo 2013/2016. Para su análisis se ha empleado una categorización deductiva-inducti-<br />va llevada a cabo con el apoyo del soporte<br />informático Atlas.ti.<br />El análisis e interpretación de los datos<br />evidencia un modelo de separación teoría<br />y práctica en el que la teoría precede a<br />la práctica y ésta es comprendida como<br />aplicación de la teoría. Una situación que<br />genera tensiones e insatisfacción entre<br />formadores –profesores y tutores- y es-<br />tudiantes, pero también la búsqueda de<br />estrategias alternativas para la co-implica-<br />ción deseable entre ambos tipos de sabe-<br />res. Sin embargo, los obstáculos son más<br />poderosos que los deseos de cambiar una<br />realidad socialmente construida en la que<br />el juego dialéctico, bidireccional, se cons-<br />tituya en principio para la acción.</p>

Frames associated with shift-invariant spaces on local fields

In this paper, we present a unified approach to the study of shift-invariant systems to be frames on local fields of positive characteristic. We establish a necessary condition and three sufficient conditions under which the shift-invariant systems on local fields constitute frames for L2(K). As an application of these results, we obtain some known conclusions about the Gabor frames and wavelet frames on local fields.

Preparation of dual-targeted redox-responsive nanogels based on pegylated sorbitan for targeted and antitumor drug delivery

This work reports the synthesis and use of a new functionalized biocompatible disulfide nanogel system based on magnetite pegylated sorbitan (PEGS), cross-linked with the amino acid N,N’-di(tert-butoxycarbonyl) cystine (N-Boc-cystine) and conjugated with folic acid (FA), to be used asan application in drug delivery systems. To achieve this purpose, Fe3O4 nanoparticles were prepared via a co-precipitation method. Star-shaped PEG that was coupled with 3-aminopropyl triethoxysilane via a Michael reaction, was grafted on the surface of iron oxide nanoparticles. The terminal hydroxyl groups on the PEG-S chain, asan efficient functional group, would easily be further modified with specific and effective groups such asactive targeting and/or cross-link agents. The carbodiimide coupling chemistry was used to conjugate FA and bind the cross-linker. To demonstrate the accuracy of each step, the structures were characterized using Fourier transform infrared spectroscopy (FTIR) spectroscopy. Thermal analysis was performed to confirm the formation of PEGS graft on the surface of the magnetite. Particle size, zeta potential and nanoparticles colloidal stability were determined by dynamic light scattering. The in vitro release behavior of 5-Fluorouracil asan anticancer drug from nanogels was investigated at pH 7.4 in phosphate-buffered saline (PBS). Folated nanogel displayed high cellular uptake into DU145 cell lines, which are distinguishable from folate-free one.

Some fixed point theorems for C*-algebra-valued b2-metric spaces

The aim of this paper is to establish the structure of C∗-algebra-valued b2-metric space and give some xed point theorems forself-maps with contractive or expansive conditions on such spaces. Asan application we investigate existence and uniqueness solution for atype of integral equation.

Estimates for coefficients of certain analytic functions

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

The mean square of the product of the Riemann zeta-function with Dirichlet polynomials

Abstract Improving earlier work of Balasubramanian, Conrey and Heath-Brown [1], we obtain an asymptotic formula for the mean-square of the Riemann zeta-function times an arbitrary Dirichlet polynomial of length T 1 2 + δ {T^{\frac{1}{2}+\delta}} , with δ = 0.01515 ⁢ … \delta=0.01515\dots . As an application we obtain an upper bound of the correct order of magnitude for the third moment of the Riemann zeta-function. We also refine previous work of Deshouillers and Iwaniec [8], obtaining asymptotic estimates in place of bounds. Using the work of Watt [19], we compute the mean-square of the Riemann zeta-function times a Dirichlet polynomial of length going up to T 3 4 {T^{\frac{3}{4}}} provided that the Dirichlet polynomial assumes a special shape. Finally, we exhibit a conjectural estimate for trilinear sums of Kloosterman fractions which implies the Lindelöf Hypothesis.

Analysis of discrete fractional operators

In this paper, we introduce two new monotonicity concepts for a nonnegative or nonpositive valued function defined on a discrete domain. We give examples to illustrate connections between these new monotonicity concepts and the traditional ones. We then prove some monotonicity criteria based on the sign of the fractional difference operator of a function f, ??f with 0 < ? < 1. As an application, we state and prove the mean value theorem on discrete fractional calculus.

On the irreducibility of locally metric connections

Abstract A locally metric connection on a smooth manifold M is a torsion-free connection D on T M with compact restricted holonomy group Hol 0 ( D ) $\mathrm {Hol}_0(D)$ . If the holonomy representation of such a connection is irreducible, then D preserves a conformal structure on M. Under some natural geometric assumption on the life-time of incomplete geodesics, we prove that conversely, a locally metric connection D preserving a conformal structure on a compact manifold M has irreducible holonomy representation, unless Hol 0 ( D ) = 0 $\mathrm {Hol}_0(D)=0$ or D is the Levi-Civita connection of a Riemannian metric on M. This result generalizes Gallot's theorem on the irreducibility of Riemannian cones to a much wider class of connections. As an application, we give the geometric description of compact conformal manifolds carrying a tame closed Weyl connection with non-generic holonomy.

A Characterisation of First-Order Constraint Satisfaction Problems

We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is first-order definable: we show the general problem to be NP-complete, and give a polynomial-time algorithm in the case of cores. A slight modification of this algorithm provides, for first-order definable CSP's, a simple poly-time algorithm to produce a solution when one exists. As an application of our algebraic characterisation of first order CSP's, we describe a large family of L-complete CSP's.

Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

This paper discusses the long time behavior of solutions for dissipative non-autonomous lattice dynamical systems. We first prove some sufficient and necessary conditions for the existence of a compact uniform attractor for the family of processes defined on a Hilbert space of infinite sequences, and then give an upper bound of the Kolmogorov $\varepsilon$-entropy for the uniform attractor. As an application, we consider the dissipative non-autonomous lattice Zakharov equations.