Martingale Solution to Stochastic Extended Korteweg-de Vries Equation

The deterministic extended Korteweg-de Vries equation plays an essential role in the description of the creation and propagation of nonlinear waves in many fields. We study a stochastic extended Korteweg-de Vries equation driven by a multiplicative noise in the form of a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied for all physically relevant initial conditions. The proof of the solution is based on two approximations of the problem considered and the compactness method.

A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type

In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.

Microstructures,Strength Characteristics and Wear Behavior of the Fe-based P/M Composites after Sintering or Infiltration with Cu–Sn Alloy

Some properties of the Fe-based P/M composites sintered and reinforced by infiltration with Cu-Sn alloy were described.It is shown that the hardness of the sintered material is 2.5 times lower,tensile strength is 1.7 times lower and the wear resistance is 2.5-3.3 times lower in comparison with those of the infiltrated material.The presence of pores on the friction surface of the sintered material affects the features of the wear process.Due to the specific morphology of copper in the infiltrated material,the phenomenon of selective mass transfer is observed and worn surfaces have a spongy-capillary texture.

Fault Detection under Fuzzy Model Uncertainty

The paper tackles the problem of robust fault detection using Takagi-Sugeno fuzzy models. A model-based strategy is employed to generate residuals in order to make a decision about the state of the process. Unfortunately, such a method is corrupted by model uncertainty due to the fact that in real applications there exists a model-reality mismatch. In order to ensure reliable fault detection the adaptive threshold technique is used to deal with the mentioned problem. The paper focuses also on fuzzy model design procedure. The bounded-error approach is applied to generating the rules for the model using available measurements. The proposed approach is applied to fault detection in the DC laboratory engine.

Acyclic colorings of graphs with bounded degree

A k coloring(not necessarily proper) of vertices of a graph is called acyclic, if for every pair of distinct colors i and j the subgraph induced by the edges whose endpoints have colors i and j is acyclic. We consider some generalized acyclic k colorings, namely, we require that each color class induces an acyclic or bounded degree graph. Mainly we focus on graphs with maximum degree 5. We prove that any such graph has an acyclic 5 coloring such that each color class induces an acyclic graph with maximum degree at most 4. We prove that the problem of deciding whether a graph G has an acyclic 2 coloring in which each color class induces a graph with maximum degree at most 3 is NP complete, even for graphs with maximum degree 5. We also give a linear time algorithm for an acyclic t improper coloring of any graph with maximum degree d assuming that the number of colors is large enough.

Unique Factorization of Compositive Hereditary Graph Properties

A graph property is any class of graphs that is closed under isomorphisms, A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs

Geographical clines in the size of the herb field mouse(Apodemus uralensis)

Patterns of body size variation along geographical gradients have long been searched for and generalized into eco-geographical rules.However,no rodent species has yet been analyzed in relation to the 3 dimensions of latitude,longitude and altitude.We analyzed geographical clines and dimorphism of body and skull size in the herb field mouse(Apodemus uralensis)across the species range,based on field data and on data from the literature.Sexual dimorphism in adult A.uralensis was not expressed at a large scale,while local patterns were inconsistent.Age-dependent size changes were most expressed in adult individuals:most characters of adults exceeded in size those of subadults,while subadult-juvenile size differences were only significant in body weight and length,zygomatic skull width,length of cranial diastema and breadth of braincase.Despite central morphological niches along the clines being separated,A.uralensis populations showed a high degree of size overlap in morphological space.We found the species to be characterized by high size variability,with the largest individuals inhabiting the eastern and southern edges of the distribution range.Tail,hind foot and ear lengths were largest in the southern part of the range,in agreement with Allen’s rule.The main measurements that we analyzed,namely body mass,zygomatic skull width and condylobasal skull length,show the presence of 3 clines in the size of adult A.uralensis:(i)a decreasing south-north cline,opposing Bergmann’s rule;(ii)an increasing west-east cline,in accordance with Murphy’s rule;and(iii)an increasing altitudinal cline.

Physics and astrophysics of strong magnetic field systems with eXTP

In this paper we present the science potential of the enhanced X-ray Timing and Polarimetry(eXTP) mission for studies of strongly magnetized objects. We will focus on the physics and astrophysics of strongly magnetized objects, namely magnetars, accreting X-ray pulsars, and rotation powered pulsars. We also discuss the science potential of eXTP for QED studies. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s.

On the Degree of Approximation of Continuous Functions by Means of Fourier Series in the Holder Metric

In this paper we prove two theorems on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series in the Holder metric.These theorems can be taken as counterparts of those previously obtained by T.Singh[3].

Continuous modeling of soil morphology—thermomechanical behavior of embankment dams

Macroscopic modeling of soils is based on a number of properties that refer to the mesoscopic morphology.The most fundamental parameters of this art are:1)coupling parameters between partial stresses of components and deformations of components,2)porosities,3)saturation,and 4)permeability and diffusivity,tortuosity.The main aim of this paper is to present in juxtaposition continuous one-,two-,and three-component models of geomaterials appearing in construction of embankment dams.In particular,the above mentioned features,especially saturation with water and seepage problems,modeling of fluidization yielding piping,and generalizations of the Darcy law and changes of porosity,are presented.

Enhanced entanglement and asymmetric EPR steering between magnons

The generation and manipulation of strong entanglement and Einstein-Podolsky-Rosen(EPR)steering in macroscopic systems are outstanding challenges in modern physics.Especially,the observation of asymmetric EPR steering is important for both its fundamental role in interpreting the nature of quantum mechanics and its application as resource for the tasks where the levels of trust at different parties are highly asymmetric.Here,we study the entanglement and EPR steering between two macroscopic magnons in a hybrid ferrimagnet—light system.In the absence of light,the two types of magnons on the two sublattices can be entangled,but no quantum steering occurs when they are damped with the same rates.In the presence of the cavity field,the entanglement can be significantly enhanced,and strong two-way asymmetric quantum steering appears between two magnons with equal dissipation.This is very different from the conventional protocols to produce asymmetric steering by imposing additional unbalanced losses or noises on the two parties at the cost of reducing steerability.The essential physics is well understood by the unbalanced population of acoustic and optical magnons under the cooling effect of cavity photons.Our finding may provide a novel platform to manipulate the quantum steering and the detection of bi-party steering provides a knob to probe the magnetic damping on each sublattice of a magnet.

The importance and potential of photovoltaics in the context of low-carbon development in Poland

The main topic of the study is the development of photovoltaic systems in Poland,and its main goal is to char-acterize the current situation and development prospects in a given subject area in the context of the growing importance of the low-carbon economy in Poland.The study uses both secondary and primary(Foresight)data.The development of photovoltaic micro-installations in Poland,recorded in recent years,was possible thanks to the state support.Unnecessary administrative barriers have been removed;legal provisions have been simplified and adapted to small,distributed systems.However,there is a risk of a slowdown in the high dynamics of rates on the analyzed market in Poland due to changes in legal solutions introduced by the state.