Existence of (Dirac-)harmonic Maps from Degenerating (Spin) Surfaces

We study the existence of harmonic maps and Dirac-harmonic maps from degenerating surfaces to a nonpositive curved manifold via the scheme of Sacks and Uhlenbeck. By choosing a suitable sequence of $$\alpha $$ α -(Dirac-)harmonic maps from a sequence of suitable closed surfaces degenerating to a hyperbolic surface, we get the convergence and a cleaner energy identity under the uniformly bounded energy assumption. In this energy identity, there is no energy loss near the punctures. As an application, we obtain an existence result about (Dirac-)harmonic maps from degenerating (spin) surfaces. If the energies of the map parts also stay away from zero, which is a necessary condition, both the limiting harmonic map and Dirac-harmonic map are nontrivial.

On some non-local approximation of nonisotropic Griffith-type functionals$ ^\dagger $

<abstract><p>The approximation in the sense of $ \Gamma $-convergence of nonisotropic Griffith-type functionals, with $ p- $growth ($ p &gt; 1 $) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on Sobolev spaces, is analysed.</p></abstract>

Multiplicity results for (p, q)-Laplacian equations with critical exponent in $${\mathbb {R}}^N$$ and negative energy

We prove existence results in all of $${\mathbb {R}}^N$$ R N for an elliptic problem of (p, q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter $$\lambda $$ λ . In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when $$\lambda $$ λ belongs to a certain interval. Our proofs use variational methods and the concentration compactness principle. Towards this aim we give a detailed proof of tight convergence of a suitable sequence.

Frequency Offset Tolerant Synchronization Signal Design in NB-IoT

Timing detection is the first step and very important in wireless communication systems. Timing detection performance is usually affected by the frequency offset. Therefore, it is a challenge to design the synchronization signal in massive narrowband Internet of Things (NB-IoT) scenarios where the frequency offset is usually large due to the low cost requirement. In this paper, we firstly proposed a new general synchronization signal structure with a couple of sequences which are conjugated to remove the potential timing error that arises from large frequency offset. Then, we analyze the suitable sequence for our proposed synchronization signal structure and discuss a Zadoff–Chu (ZC) sequence with root 1 as an example. Finally, the simulation results demonstrate that our proposed synchronization signal can work well when the frequency offset is large. It means that our proposed synchronization signal design is very suitable for the massive NB-IoT.

Automatic Composition of Instructional Units in Virtual Learning Environments

In this paper, a new approach for automatic composition of instructional units based on a new variant of Harmony Search Algorithm is proposed. The purpose is to solve curriculum sequencing issue by designing and arranging learning content in a suitable sequence. By suitable sequence we mean a learning sequence that fits learner level and presents the content in a way that conveys its structure to learner. Results show that the proposed approach is promising. For instance, individualized courseware plan are generated “on the spot” carefully considering both students characteristics and subject-matter coherence.

Recursive interpolating sequences

This paper is devoted to pose several interpolation problems on the open unit disk 𝔻 of the complex plane in a recursive and linear way. We look for interpolating sequences (zn) in 𝔻 so that given a bounded sequence (an) and a suitable sequence (wn), there is a bounded analytic function f on 𝔻 such that f(z1) = w1 and f(zn+1) = anf(zn) + wn+1. We add a recursion for the derivative of the type: f′(z1) = $\begin{array}{} w_1' \end{array} $ and f′(zn+1) = $\begin{array}{} a_n' \end{array} $ [(1 − |zn|2)/(1 − |zn+1|2)] f′(zn) + $\begin{array}{} w_{n+1}', \end{array} $ where ($\begin{array}{} a_n' \end{array} $) is bounded and ($\begin{array}{} w_n' \end{array} $) is an appropriate sequence, and we also look for zero-sequences verifying the recursion for f′. The conditions on these interpolating sequences involve the Blaschke product with zeros at their points, one of them being the uniform separation condition.

A Remark on Topological Sequence Entropy

Let [Formula: see text] be the supremum of all topological sequence entropies of a dynamical system [Formula: see text]. This paper obtains the iteration invariance and commutativity of [Formula: see text] and proves that if [Formula: see text] is a multisensitive transformation defined on a locally connected space, then [Formula: see text]. As an application, it is shown that a Cournot map is Li–Yorke chaotic if and only if its topological sequence entropy relative to a suitable sequence is positive.

A justification of the Timoshenko beam model through Γ-convergence

We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of [Formula: see text]-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence [Formula: see text]-converges to a functional representing the energy of a Timoshenko beam.

COMPUTATION OF GREEKS FOR JUMP-DIFFUSION MODELS

In the present paper, we compute the Greeks for a class of jump diffusion models by using Malliavin calculus techniques. More precisely, the model under consideration is governed by a Brownian component and a jump part described by a compound Poisson process. Our approach consists of approximating the compound Poisson process by a suitable sequence of standard Poisson processes. The Greeks of the original model are obtained as limits or weighted limits of the Greeks of the approximate model. We illustrate our results by the computation of the Greeks for digital options in the framework of the Merton model. The technique of Malliavin weights is found to be efficient compared to the finite difference approach.