Coreness of Cooperative Games with Truncated Submodular Profit Functions

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot)$ is defined by a truncation of a submodular function $\sigma(\cdot)$: $f(\cdot)=\sigma(\cdot)$ if $\sigma(\cdot)\geq\eta$ and $f(\cdot)=0$ otherwise, where $\eta$ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value

Study of decagonal approximant and γ-brass-type compounds in Al-Cr-Fe thin films

This paper reports the preparation conditions and structure characteristics of Al-Cr-Fe very thin films (10-30 nm) obtained by the flash evaporation technique. The films are either amorphous or crystallized, depending on the thickness of the sample and temperature of the substrate. Annealing of amorphous films leads to crystallization of intermetallic phases that are all linked with quasicrystals. In particular, we have identified by transmission electron microscopy the following structures: body-centered-cubic (bcc) γ-brass phase, monoclinic λ-Al13(Cr,Fe)4 phase, and orthorhombic O1-phase, all of them already observed in this system, together with four new structures, i.e., a face-centered-cubic (fcc) γ-brass phase (superstructure of the bcc phase), monoclinic λ′-phase (related to the λ-phase) and two orthorhombic phases (1/1/; 1/1) and (1/0; 2/1) approximants of the decagonal phase). In this study, we point out the occurrence of twin defects of the λ-Al13(Cr,Fe)4 phase. Films prepared directly in the crystalline state comprise the O1 approximant. Electron energy loss spectroscopy measurements show that all films are not oxidized except for the presence of a native oxide layer that forms in ambient atmosphere with a thickness that cannot exceed 0.3 nm. Optical properties were investigated and show that films need to be large enough (>30 nm) to reproduce the properties of bulk alloys. Finally, contact angle wetting measurements reveal that the presence of such films on a substrate, even at very low thickness, considerably decreases the wetting behavior by wate

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling. An adaptive cell size method is introduced into the enthalpy method to mitigate against `narrow-band features' that can introduce significant error. By using this technique an excellent agreement is found between the enthalpy method and the analytic theory for solidification of pure nickel

Quantum catastrophes: a case study

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.Comment: 23 p

A stable dendritic growth with forced convection: A test of theory using enthalpy-based modeling methods

The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its tip velocity increases with increasing fluid velocity

Theoretical modeling of crystalline symmetry order with dendritic morphology

The stable growth of a crystal with dendritic morphology with n-fold symmetry is modeled. Using the linear stability analysis and solvability theory, a selection criterion for thermally and solutally controlled growth of the dendrite is derived. A complete set of nonlinear equations consisting of the selection criterion and an undercooling balance (which determines the implicit dependencies of the dendrite tip velocity and tip diameter on the total undercooling) is formulated. The growth kinetics of crystals having different lattice symmetry is analyzed. The model predictions are compared with phase field modelling data on ice dendrites grown from pure undercooled water

THE ROLE OF FLUID VELOCITY ON THE SHAPE OF DENDRITIC TIPS

This study is concerned the shape of dendritic tip grown from an undercooled melt in the presence of fluid velocity. The tip shape function is derived and tested against numerical simulations when a forced convection plays a decisive role.L.V.T. acknowledges the financial support from the Russian Science Foundation (project no. 21-79-10012)