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Search results for: G-SPACE
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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublicationIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublicationIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Deterministic Rendezvous in Restricted Graphs
PublicationIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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Investigating lubricants behaviour in microgravity for vibration damping purposes
PublicationVibration is one of the harshest environments an object is exposed to during and after launch into space on a launch vehicle. Such vibrations should be damped to avoid destruction of the spacecraft or its elements. Currently, active and material damping is used. A possibility of using lubrication as the damping factor is suggested by some research. MoS2 is a typical solid lubricant used in space applications. Its properties vary...
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublicationLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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Investigation of the Effect of the Rocket's Suborbital Flight on Biofilm, Enzymes and Biosynthesis on Autonomous, Modular and Scalable Platforms For Conducting Experiments of an Astrobiotechnological Nature
PublicationWith new incentives for human space exploration, biotechnological experiments in orbit became imperative. Answering this need, we build an autonomous, modular, and scalable platform that enables those experiments on rockets. We called it AMBER. The aim of the payload of the R6 suborbital rocket is to perform an experiment to study the influence of rocket flights on biofilm, molecular biology enzymes and biosynthesis using our platform....
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Multi-Beam Antenna for Ka-Band CubeSat Connectivity Using 3-D Printed Lens and Antenna Array
PublicationIn this paper, the design of a passive multi-beam lens antenna is proposed for the CubeSat space communication system as an alternative application of a 2-D microstrip antenna array that has originally been designed for a 39 GHz 5 G MU-MIMO system. The half-ellipsoid lens is 3-D printed using stereolithography (SLA) technology. The antenna prototype is capable of selecting the main beam between 16 different directions with a gain...
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Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations
PublicationAbstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version...
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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White Rabbit in space related application
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INVESTIGATION OF THE EFFECT OF THE ROCKET'S SUBORBITAL FLIGHT ON BIOFILM, ENZYMES AND BIOSYNTHESIS ON AUTONOMOUS, MODULAR AND SCALABLE PLATFORM FOR CONDUCTING EXPERIMENTS OF AN ASTROBIOTECHNOLOGICAL NATURE
PublicationWith new incentives for human space exploration, biotechnological experiments in orbit became imperative.Answering this need, we build an autonomous, modular, and scalable platform that enables those experiments onrockets. We called it AMBER. The aim of the payload of the R6 suborbital rocket is to perform an experiment tostudy the influence of rocket flights on biofilm, molecular...
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Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios
PublicationThe problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes...
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublicationUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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Vibrational inelastic electron-H2 scattering revisited: numerically converged coupled channels space frame calculations with model interaction
PublicationZderzeniowe wzbudzenie niższych oscylacyjnych poziomów molekuły H2 (^1Σ^+,g) przez elektrony o niskiej energii. Obliczenia wykonano przy użyciu empirycznego modelowego potencjału oraz przez rozwiązanie równania rozpraszania dwukanałowego w układzie współrzędnych, związanych z molekułą.
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A Compact Circularly Polarized Antenna With Directional Pattern for Wearable Off-Body Communications
PublicationThis letter presents a geometrically simple and compact circularly polarized (CP) antenna with unidirectional radiation characteristics for off-body communications. The proposed antenna is based on a microstrip line monopole extension from a coplanar waveguide (CPW) and a protruded stub from one side of the coplanar ground plane along the length of the monopole. The orthogonal components of equal amplitudes required for circular...