In this work we classify all smooth surfaces with geometric genus equal to three and an action of a group G isomorphic to (Z/2)^k such that the quotient is a plane. We find 11 families. We compute the canonical map of all of them, finding in particular a family of surfaces with canonical map of degree 16 that we could not find in the literature. We discuss the quotients by all subgroups of G finding several K3 surfaces with symplectic involutions. In particular we show that six families are families of triple K3 burgers in the sense of Laterveer.
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly in characteristic $0$, but we also see the tweaks which extend most of the content to analytic and differential settings.
This manuscript deals with a hyperbolic partial differential equation with fractional differential and fractional integral forcing functions. Semidiscretization method is used to establish a unique strong solution and also approximate solutions. Error estimates and continuous dependence of the strong solution on the given conditions have also been discussed. At the end, we illustrated the results with an example.
The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).
Using the notion of tame regular $d$-path of the topological $n$-cube, we introduce the tame regular realization of a precubical set as a multipointed $d$-space. Its execution paths correspond to the nonconstant tame regular $d$-paths in the geometric realization of the precubical set. The associated Moore flow gives rise to a functor from precubical sets to Moore flows which is weakly equivalent in the h-model structure to a colimit-preserving functor. The two functors coincide when the precubical set is spatial, and in particular proper. As a consequence, it is given a model category interpretation of the known fact that the space of tame regular $d$-paths of a precubical set is homotopy equivalent to a CW-complex. We conclude by introducing the regular realization of a precubical set as a multipointed $d$-space and with some observations about the homotopical properties of tameness.
A new method to find first integrals of nonlinear differential equations in Jacobi-type form is presented. The basic idea of our approach is to use one-parameter perturbed motions to find well-conceived nonlocal constants that are conserved along solutions. By means of such nonlocal framework we derive a set of theorems that we apply to look for the first integrals of some relevant cases, where moreover a solution is obtained. Applications also include some equations of the Painlevé-Gambier classification.
We consider a family of Euler-type polynomials, depending on a real parameter α 6= 0, 1. The case α = 2 corresponds to standard Euler polynomials. We show some properties of these polynomials, and show also two generalized recurrences. As consequences of these results, we obtain several explicit formulas for Euler numbers and polynomials.
Strong convergence theorems that approximate common fixed points of two nonlinear mappings are presented. Our method is based on the Martinez-Yanes–Xu iteration, which extends Nakajo and Takahashi’s CQ method. In this paper, by exploiting the mean-valued iteration procedure, we further develop Nakajo and Takahashi’s CQ method and Takahashi, Takeuchi, and Kubota’s shrinking projection method. The approach of this paper does not require that the two mappings be continuous or commutative. The types of mappings considered in this paper include nonexpansive mappings and other well-known classes of mappings as special cases.
Seasonality due to environmental influences often affects contact between species for food or shelter as well as the spread and persistence of diseases from those vector species. Epidemic models may capture seasonality patterns in a phenomenological way by making the epidemiological parameters and the population demographics are time-periodic. A mathematical model with these features for the dengue fever is analyzed, to such an extent that the threshold between uniform persistence and extinction of the disease is established, that is: there exists a unique positive disease-free periodic solution being globally asymptotically stable when the basic reproductive number is greater that one, but it is unstable when the basic reproductive number is less than one, in whose situation there exists at least one non-trivial positive periodic solution and dengue fever is endemic in the community. At last, numerical simulations are carried out to illustrate the theoretical results.
Abstract. This paper is concerned with the study of the non-coercive p(x)-parabolic problems. We prove the existence of entropy solutions for this parabolic equation, and we will conclude some regularity results.
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas' results giving sufficient criteria for the existence of formal smoothings.
This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions, which are particularly nice cofibrations. The cobar construction of a locally conilpotent cocommutative coalgebra is shown to be an example of semifree DG-Lie algebra. We also give an example of a non-cofibrant DG-Lie algebra whose underlying graded Lie algebra is free; this cannot occur in the bounded above case, where DG-Lie algebras of this form are always cofibrant.
In this paper, we interest on some class of Stefan type problems. We prove the existence and uniqueness of renormalized solution in anisotropic Sobolev spaces with data belongs to $L^1- data,$ based on the properties of the renormalized trunctions and the generalized monotonicity method in the functional spaces.
In this paper, a new family of rotationally symmetric planar graphs is described based on an edge coalescence of planar chorded cycles. Their local fractional metric dimension is established for those ones arisen from chorded cycles of order up to six. Their asymptotic behaviour enables us to ensure the existence of new families of rotationally symmetric planar graphs with either constant or bounded local fractional dimension.
We consider the numbers $\mathcal{B}_{r,s} = (\mathbf{B}+1)^r \mathbf{B}^s$ (in umbral notation $\mathbf{B}^n = \mathbf{B}_n$ with the Bernoulli numbers) that have a well-known reciprocity relation, which is frequently found in the literature and goes back to the 19th century. In a recent paper, self-reciprocal Bernoulli polynomials, whose coefficients are related to these numbers, appeared in the context of power sums and the so-called Faulhaber polynomials. The numbers $\mathcal{B}_{r,s}$ can be recursively expressed by iterated sums and differences, so it is not obvious that these numbers do not vanish in general. As a main result among other properties, we show the non-vanishing of these numbers, apart from exceptional cases. We further derive an explicit product formula for their denominators, which follows from a von Staudt--Clausen type relation.
This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that $${\frac{\pi }{\left( e^{-\left\vert x\right\vert ^{2}}+\left\vert u\right\vert +\left\vert b\right\vert \right) ^{\theta }}\in L}^{p}(0,T;L^{q,\infty }(\mathbb{R}^{3})),\text{ where }\frac{2}{p}+\frac{3}{% q}=2-\theta \text{ and }0\leq \theta \leq 1.$$
This article proposes a mathematical model describing the evolution and transmission of Varicella Zoster Virus (VZV) over large groups of individuals. The model was formulated to accommodate parameters and variables describing direct and indirect forms of transmission, re-activation of infectious shingles as well as treatment and vaccination of susceptible births and influx of immigrants. The model was analysed to be positive, bounded and well posed. The controlled basic reproduction number Rvzv, obtained using the next generation matrix operator reveal that vaccination is effective as a control in creating a level herd immunity. Linearizing the model around the VZV - free equilibrium shows that the model is locally and globally asymptotically stable when Rvzv is less than unity. The approximate solutions of the model system equations was obtained using the modified differential transform which involves the Differential Transform Method (DTM) and Laplace - Pade post-treatment technique (LPDTM). This technique was employed to enlarge the domain of convergence of the approximate solutions of the model. LPDTM was compared with the Fehlberg fourth order Runge - Kutta (RKF45) via the MAPLE computational software to show the accuracy of the results through simulations. Further simulations carried out on the model reveal that timely vaccination and treatment are eeffective strategies in containing VZV infection spread in human and environmental host population.
We provide complementary semiclassical bounds for the Riesz means R1(z) of the eigenvalues of various biharmonic operators, with a second term in the expected power of z. The method we discuss makes use of the averaged variational principle (AVP), and yields two-sided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.
We consider an abstract Cauchy problem of an evolution inclusion with a singlevalued perturbation on a real Hilbert space. The evolution inclusion contains subdifferentials of time-dependent, proper, lower semicontinuous, convex functions which depends on a solution itself of the Cauchy problem. Moreover, the subdifferentials are taken with respect to inner products, which also depend on a solution of the Cauchy problem. Such structures are sometimes called quasi-variational structures for convex functions and inner products. The main purposes of this paper are to show the existence of strong solutions to the Cauchy problem of an evolution inclusion with a perturbation and to apply this result to a mass-conservative tumor invasion model with a degenerate cross diffusion.
We prove an asymptotic behavior result of entropy solutions to fractional parabolic problems whose simplest model is (P) ( ut(t, x) + (−∆)s pu(x) = µ in Q := (0, T) × Ω, u(0, x) = u0(x) in Ω, u(t, x) = 0 on Σ := (0, T) × ∂Ω, where, Ω is a bounded domain of RN (N ≥ 2), T > 0, (−∆)s pu is the fractional p-Laplace operator (ps < N, 0 < s < 1), p > 2 − s N , µ ∈ M+(Q) is a nonnegative measure with bounded variation over Q and u0 ∈ L1 (Ω) is a nonnegative function. We first prove some a priori estimates on the entropy solutions, we then show that, if µ does not depend on time, then the sequence of entropy solutions of such problems converge to the stationary solution of the corresponding elliptic problem as t tends to infinity.
