Weight 2 CM newforms as p-adic limits

The Ramanujan Journal - Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application of the U-operator. The proofs of...     

Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited

Micromechanical deformation phenomena such as those leading to macroscopic viscoelastic and plastic behavior must be studied from a thermodynamic viewpoint, as they induce complex and partly irreversible heat effects. Calorimetric measurements of the intrinsic volumetric thermomechanical heat sources (THS) activated in the material bulk during mechanical loads can produce valuable information with respect to that aim. They can be based on infrared imaging if submitted to inverse algorithms that allow a correct reconstruction of THS to be produced. Here, an inverse method relying on a diffusion-advection heat transfer model is applied to experimental temperature maps recorded during tensile tests. These are made on a semi-crystalline polymer that shows a strong development of plastic instabilities. Along with simultaneous kinematic observables produced with a digital image correlation system, the competition between advection and diffusion phenomena may be clearly established. 1-D profiles of the reconstructed THS and measured strain rates illustrate clearly that thermomechanical effects associated with necking onset and propagation follow the kinematic variable in a rather direct manner. Finally, we show for tensile experiments that THS estimations lead to analyze plasticity as a rheological behavior controlled by the flow stress, responsible of necking development and propagation.     

The presence of symplectic strata improves the Gevrey regularity for sums of squares

We consider a class of operators of the type sum of squares of real analytic vector fields satisfying the Hörmander bracket condition. The Poisson-Treves stratification is associated to the vector fields. We show that if the deepest stratum in the stratification, i.e., the stratum associated to the longest commutators, is symplectic, then the Gevrey regularity of the solution is better than the minimal Gevrey regularity given by the Derridj-Zuily theorem.     

Orienteering for electioneering

In this paper, we introduce a combinatorial optimization problem that models the investment decision a political candidate faces when treating his or her opponents’ campaign plans as given. Our formulation accounts for both the time cost of traveling between districts and the time expended while campaigning within districts. We describe a polynomial-time algorithm that computes a $(2+?)$-approximation to the optimal solution of a discrete version of our problem by reducing the problem to another combinatorial optimization problem known as Orienteering.     

PIV Measurements of a Turbulent Boundary Layer Perturbed by a Wall-Mounted Transverse Circular Cylinder Element

Postprocessing and storage of large data sets represent one of the main computational bottlenecks in computational fluid dynamics. We assume that the accuracy necessary for computation is higher than needed for postprocessing. Therefore, in the current work we assess thresholds for data reduction as required by the most common data analysis tools used in the study of fluid flow phenomena, specifically wall-bounded turbulence. These thresholds are imposed a priori by the user in L₂-norm, and we assess a set of parameters to identify the minimum accuracy requirements. The method considered in the present work is the discrete Legendre transform (DLT), which we evaluate in the computation of turbulence statistics, spectral analysis and resilience for cases highly-sensitive to the initial conditions. Maximum acceptable compression ratios of the original data have been found to be around 97%, depending on the application purpose. The new method outperforms downsampling, as well as the previously explored data truncation method based on discrete Chebyshev transform (DCT).     

Adjoining batch Markov arrival processes of a Markov chain

A batch Markov arrival process (BMAP) X* = (N, J) is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper, a new and inverse problem is proposed firstly: given a Markov chain J, can we deploy a process N such that the 2-dimensional process X* = (N, J) is a BMAP? The process X* = (N, J) is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed (i.i.d) random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic (D _k , k = 0, 1, 2 · · ·) and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.     

Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel

Making use of the traditional Caputo derivative and the newly introduced Caputo-Fabrizio derivative with fractional order and no singular kernel, we extent the nonlinear Kaup-Kupershmidt to the span of fractional calculus. In the analysis, different methods of fixed-point theorem together with the concept of piccard L-stability are used, allowing us to present the existence and uniqueness of the exact solution to models with both versions of derivatives. Finally, we present techniques to perform some numerical simulations for both non-linear models and graphical simulations are provided for values of the order α = 1.00; 0.90. Solutions are shown to behave similarly to the standard well-known traveling wave solution of Kaup-Kupershmidt equation.     

Constrained Extremum Problems,Regularity Conditions and Image Space Analysis. Part I: The Scalar Finite-Dimensional Case

Image space analysis has proved to be instrumental in unifying several theories, apparently disjoint from each other. With reference to constraint qualifications/regularity conditions in optimization, such an analysis has been recently introduced by Moldovan and Pellegrini. Based on this result, the present paper is a preliminary part of a work, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. The present part deals with scalar constrained extremum problems in a Euclidean space. The vector case as well as the case of infinite-dimensional image will be the subject of a subsequent part.     

Images and Existence of Constrained Scalar and Vector Extrema

By means of the image space analysis, a necessary and sufficient condition is established for the existence of vector extrema. In the scalar case, the sufficient part is shown to shrink to a known one.