Analogue Of Space Research Articles

Generalized solutions and generalized eigenfunctions of boundary-value problems on a geometric graph

We consider generalized solutions to boundary-value problems for elliptic equations on an arbitrary geometric graph and their corresponding eigenfunctions. We construct analogs of Sobolev spaces that are dense in L2. We obtain conditions for the Fredholm solvability of boundary-value problems of various types, describe their spectral properties and conditions for the expansion in generalized eigenfunctions. The results presented here are fundamental in studying boundary control problems of oscillations of multiplex jointed structures consisting of strings or rods, as well as in studying the cell metabolism.

The temperature effect on the glycine decomposition induced by 2 keV electron bombardment in space analog conditions

Glycine is the simplest proteinaceous amino acid that has been extensively detected in carbonaceous meteorites and was recently observed in the cometary samples returned to Earth by NASA’s Stardust spacecraft. In space, such species is exposed to several radiation fields at different temperatures. In aqueous solutions, this species appears mainly as zwitterionic glycine (+NH3CH2COO−) however, in solid phase, it may be found in amorphous or crystalline forms. Here, we present an experimental study on the destruction of two zwitterionic glycine crystals (α- and β-form) at two different temperatures (300 K and 14 K) by 2 keV electrons in an attempt to test the behavior and stability of this molecular species in different space environments. The samples were analyzed in situ by Fourier transform infrared spectrometry at electron fluences. The experiments were carried out under ultra-high vacuum conditions at the Molecular Physics Laboratory at the Open University at Milton Keynes, UK. The dissociation cross section of glycine is approximately 5 times higher for the 14 K samples when compared to the 300 K samples. In contrast, no significant differences emerged between the dissociation cross sections of α- and β-forms of glycine for fixed temperature experiments. We therefore conclude that the destruction cross section is more heavily dependent on temperature than the phase of the condensed glycine material. This may be associated with the opening of additional reaction routes in the frozen samples involving the trapped daughter species (e.g. CO2 and CO). The half-life of studied samples extrapolated to space conditions shows that glycine molecules on the surface of interstellar grains has less survivability and they are highly sensitive to ambient radiations, however, they can survive extended period of time in the solar system like environments. Survivability increases by a factor of 5 if the samples are at 300 K when compared to low temperature experiments at 14 K and is independent of the crystalline structure. In addition, this survival would increase if the molecular species were protected by several layers of other molecular species as trapped in comet mantles or embedded within regolith in asteroids/lunar surfaces. The understanding of the excitation and dissociation processes of organic compounds in space simulation is highly required to put constrains in the puzzle over the origin of life in the primitive Earth.

Stress and Recovery Responses during a 105‐day Ground‐based Space Simulation

The present study analysed the time course of the psychological process of stress and recovery in six healthy male volunteers during the Mars 105 experimentation, a 105-day ground-based space analogue. The multidimensional assessment of stress and recovery responses showed that stress levels decreased significantly throughout the 105-day isolated and confined extreme (ICE) experiment, especially on its social dimension. In line with previous studies, Fatigue showed a global and progressive reduction. The present results suggest that ICE exposure may not systematically induce stress overload and impaired psychological states. To optimize adaptation to ICE conditions, further improvements in positive psychological effects may be possible by improving the countermeasures, as well as the screening and selection of participants, in order to enhance coping capacities and to improve the balance of recovery-stress states.

Observing Dirac’s Classical Phase Space Analog to the Quantum State

In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum state of the transverse degree of freedom of a photon by weakly measuring transverse x so as to not randomize the subsequent p measurement. Furthermore, we show that the distribution has the classical-like feature that it transforms (e.g., propagates) according to Bayes’ law.

Terrestrial stress analogs for spaceflight associated immune system dysregulation

Recent data indicates that dysregulation of the immune system occurs and persists during spaceflight. Impairment of immunity, especially in conjunction with elevated radiation exposure and limited clinical care, may increase certain health risks during exploration-class deep space missions (i.e. to an asteroid or Mars). Research must thoroughly characterize immune dysregulation in astronauts to enable development of a monitoring strategy and validate any necessary countermeasures. Although the International Space Station affords an excellent platform for on-orbit research, access may be constrained by technical, logistical vehicle or funding limitations. Therefore, terrestrial spaceflight analogs will continue to serve as lower cost, easier access platforms to enable basic human physiology studies. Analog work can triage potential in-flight experiments and thus result in more focused on-orbit studies, enhancing overall research efficiency. Terrestrial space analogs generally replicate some of the physiological or psychological stress responses associated with spaceflight. These include the use of human test subjects in a laboratory setting (i.e. exercise, bed rest, confinement, circadian misalignment) and human remote deployment analogs (Antarctica winterover, undersea, etc.) that incorporate confinement, isolation, extreme environment, physiological mission stress and disrupted circadian rhythms. While bed rest has been used to examine the effects of physical deconditioning, radiation and microgravity may only be simulated in animal or microgravity cell culture (clinorotation) analogs. This article will characterize the array of terrestrial analogs for spaceflight immune dysregulation, the current evidence base for each, and interpret the analog catalog in the context of acute and chronic stress.

Conditions C_p, C'_p, and C''_p for p-operator spaces

Conditions $C$, $C'$, and were introduced for operator spaces in an attempt to study local reflexivity and exactness of operator spaces (Effros and Ruan, 2000). For example, it is known that an operator space $W$ is locally reflexive if and only if $W$ satisfies condition (Effros and Ruan, 2000) and an operator space $V$ is exact if and only if $V$ satisfies condition $C'$ (Effros and Ruan, 2000). It is also known that an operator space $V$ satisfies condition $C$ if and only if it satisfies conditions $C'$ and (Effros and Ruan, 2000, and Han, 2007). In this paper, we define $p$-operator space analogues of these definitions, which will be called conditions $C'_p$, and $C_p$, and show that a $p$-operator space on $L_p$ space satisfies condition $C_p$ if and only if it satisfies both conditions $C'_p$ and $C_p$. The $p$-operator space injective tensor product of $p$-operator spaces will play a key role.

Formula omitted]-nuclearity, traces, and Grothendieck–Lidskii formula on compact Lie groups

Given a compact Lie group G, in this paper we give symbolic criteria for operators to be nuclear and r-nuclear on Lp(G)-spaces, with applications to distribution of eigenvalues and trace formulae. Since criteria in terms of kernels are often not effective in view of Carleman's example, in this paper we adopt the symbolic point of view. The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space G×Gˆ, where Gˆ is the unitary dual of G. No regularity of the kernel (or of the symbol) is assumed so that several of the obtained criteria extend to the more general setting of compact topological groups.

THE TRANSLATION THEOREM ON THE GENERALIZED ANALOGUE OF WIENER SPACE AND ITS APPLICATIONS

In this note, we prove the translation theorem for the generalized analogue of Wiener measure space and we show some properties of the generalized analogue of Wiener measure from it. 1. Preliminaries Wiener proved the existence theorem of the measure mw, based on the properties of Brownian motion, on the space C0(0;T), the space of all real-valued continuous functions on a closed bounded interval (0;T) which vanish at 0 in 1923. This space C0(0;T) is called the Wiener space (8). The theories for this space were studied extensively and applied to various mathematical subjects by too many mathematicians. The theories of the generalized Wiener measure space (C0(0;T);ma;b), where a : (0;T) !R is continuous and b : (0;T) !R is strictly increas- ing continuous, were developed by S.J. Chang, D.M. Chung and D.L. Skoug in (2, 5). The generalized Wiener measure space is a kind of generalization of the concrete Wiener measure space. The author and Im introduced the deflnition and several properties of analogue of Wiener measure on the space C(0;T) with the uniform topology, the space of all real-valued continuous function on (0;T) in (6). The analogue of Wiener measure space (C(0;T);m') is another generalization of the concrete Wiener measure space. In 2010, the author presented the deflnition and some properties of generalized analogue of Wiener measure space (C(0;T);ma;b;') in (7). This is the generalization of the concrete Wiener measure space, including both concepts of the

The space [formula omitted] on a surface – Application to Donati-like compatibility conditions on a surface

In this Note, we show how the analogue of the classical space H(div,⋅) can be defined on a surface. We then establish several properties of this space, notably the existence of a basic Greenʼs formula satisfied by its elements. These results are then used for identifying Donati-like compatibility conditions on a surface.

Essential normality of polynomial-generated submodules: Hardy space and beyond

Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [11]. Using improved techniques, we show that the Hardy space analogue of this result holds, and more.

Analogs of S-type spaces of partially even functions

We construct analogs of S-type spaces whose elements are functions even in certain parts of components of their arguments. We deduce a formula expressing the power of a Bessel operator via the corresponding powers of differential operators. The proposed formula enables us to establish the relationship between these spaces in terms of the Fourier–Bessel transformation and to clarify some basic properties of typical operations over their elements.

Fractional order Sobolev classes on infinite-dimensional spaces

1 In this paper we study fractional order Sobolev classes, including some analogues of Besov spaces on infinitedimensional spaces with Gaussian measures. We obtain a number of results of the embedding theo� rem type. For defining fractional classes, as in the works (1, 2), we use the interpolation approach. In the work (3), a different definition of Besov classes on finitedimensional spaces with Gaussian measures has been given. This definition can be extended to infinite� dimensional spaces with Gaussian measures as well. As shown below, for some series of parameters, the interpolation Besov classes coincide with the spaces defined by the method proposed in (3).

Quadratic variation of martingales in Riesz spaces

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales.

Skeletally Dugundji spaces

Abstract We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)] consisting of skeletal maps.

A note on the Manickam–Miklós–Singhi conjecture

For k∈Z+, let f(k) be the minimum integer N such that for all n≥N, every set of n real numbers with nonnegative sum has at least (n−1k−1)k-element subsets whose sum is also nonnegative. In 1988, Manickam, Miklós, and Singhi proved that f(k) exists and conjectured that f(k)≤4k. In this note, we prove f(3)=11, f(4)≤24, and f(5)≤40, which improves previous upper bounds in these cases. Moreover, we show how our method could potentially yield a quadratic upper bound on f(k). We end by discussing how our methods apply to a vector space analogue of the Manickam–Miklós–Singhi conjecture.

Twistor Geometry of a Pair of Second Order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature $(2, 2)$. We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti--self--dual structures with conformal symmetry algebra of the same dimension. Some of these examples are $(2, 2)$ analogues of plane wave space--times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.

Geometry of discrete quantum computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space ) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to , the discrete analogue of the complex projective space, which has irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field have pn(p − 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p − 1)(p + 1)n − 1 maximally entangled states with purity zero.

A crossed product approach to Orlicz spaces

We show how the known theory of non-commutative Orlicz spaces for semifinite von Neumann algebras equipped with an faithful normal semifinite trace may be recovered using crossed product techniques. Then using this as a template, we construct analogues of such spaces for type III algebras. The constructed spaces naturally dovetail with and closely mimic the behaviour of Haagerup Lp-spaces. We then define a modified K-method of interpolation which seems to better fit the present context, and give a formal prescription for using this method to define what may be regarded as type III Riesz–Fischer spaces.

Well-posedness of fractional parabolic equations

In the present paper, we consider the abstract Cauchy problem for the fractional differential equation 1 in an arbitrary Banach space E with the strongly positive operators . The well-posedness of this problem in spaces of smooth functions is established. The coercive stability estimates for the solution of problems for 2m th order multidimensional fractional parabolic equations and one-dimensional fractional parabolic equations with nonlocal boundary conditions in a space variable are obtained. The stable difference scheme for the approximate solution of this problem is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is established. In practice, the coercive stability estimates for the solution of difference schemes for the fractional parabolic equation with nonlocal boundary conditions in a space variable and the 2m th order multidimensional fractional parabolic equation are obtained. MSC:65M12, 65N12.

On the Topological and Uniform Structure of Diversities

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note, we consider the analytical properties of diversities, in particular the generalizations of uniform continuity, uniform convergence, Cauchy sequences, and completeness to diversities. We develop conformities, a diversity analogue of uniform spaces, which abstract these concepts in the metric case. We show that much of the theory of uniform spaces admits a natural analogue in this new structure; for example, conformities can be defined either axiomatically or in terms of uniformly continuous pseudodiversities. Just as diversities can be restricted to metrics, conformities can be restricted to uniformities. We find that these two notions of restriction, which are functors in the appropriate categories, are related by a natural transformation.