Cut elimination is the main tool in proof theoretical research. The emphasis there, however, is on the cut–elimination procedure, i.e., the dynamical aspect of cut–elimination. In this paper we want to show that also the statical aspect, i.e., the mere existence of cut–free derivations, has consequences which may be viewed to belong to Descriptive Set Theory or Generalized Recursion Theory. We ...

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free poin...

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.

This paper gives a proof of existence of price equilibria under certain parameters for a model of product differentiation commonly used in the empirical geographic differentiation literature. This proof is needed because the assumptions of Caplin and Nalebuff (1991) are not generally satisfied once data is introduced to geographic models. The theorem also has implications for existence in mixed...

Bio-mimetic Robotics often deploys locomotion mechanisms (swimming, crawling, flying etc...) which rely on repetitive patterns for the actuation schemes. This directly translates into periodic forcing inputs for the dynamics of the mechanical system. Closed loop control is achieved by modulating shape-parameters (e.g. duty cycle) which directly affect the mean values of the forcing inputs. In t...

The abstract economy defined by Debreu (1952) generalizes the Nash non-cooperative game in that a player’s strategy set depends on the strategy choices of all the other players. Debreu (1952) proved the existence of equilibrium in abstract economies with finitely many agents, finite dimensional strategy space, and quasi-concave utility functions. Since then, the Debreu’s result has been extende...

see section 4 for an account of a few examples. In (∗), q describes the input and possibly output of one agent, r the output (i.e., removal) and possibly input of a second agent, and u and v describe some mechanism of conversion of the first agent to the second agent (e.g., in an enzyme reaction or a population model). ε is a scaling parameter. We are interested in boundedness of the solutions,...

We study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the term is generalization existing results. Making use some important boundedness properties Calder\'on-Zygmund operator \(L_p\) Lipschitz spaces, we obtain local global existence theorems.

Existence and boundedness is proved for the solutions of boundary value problems resulting from modelling a flow in rectangular box by four velocity Broadwell model. The influence orientation model relation to sides rectangle on form problem analysed. uniqueness maxwellian proved. non established building different exact same macroscopic density.