## What is/are One Space?

One Space - The animals rapidly acquired the ability to identify their target, ultimately allowing them to cooperate by moving from one space to another voluntarily.^{[1]}In a previous paper, we obtained several"compact versions"of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded.

^{[2]}The results can be generalized in specified spaces as soft Banach space, soft metric space for rational contraction, soft s metric space, soft b metric space, soft cone space, random soft Banch spaces.

^{[3]}The one space, one time (1+1) nonlinear Schrödinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions.

^{[4]}OBJECTIVE The authors aimed to determine the efficacy of open-door laminoplasty with stand-alone autologous bone spacer for preserving enlarged lamina in patients with cervical myelopathy.

^{[5]}In the present work, we search a new exact solution of Einstein’s field equations using Karmarkar condition of embedded class one space time.

^{[6]}The whole circumference zone space that encloses all the sampling data points is divided into different subzones to determine the target candidate feature points, which are used for constructing the MCC or MIC.

^{[7]}The novelty of the paper is the generalization of already known results in the one space dimension to the multidimensional case.

^{[8]}The national development of any multicultural society is associated with a number of problems and challenges, because such a society is a set of different cultures that exist in one space and means the ability of people of different national, religious and cultural backgrounds to live in a single territory.

^{[9]}We consider the Cauchy problem for the higher-order nonlinear nonlocal Schrodinger equation in one space dimension i ∂ t u − Λ u = λ u 3 u , t > 0 , x ∈ R , u 0 , x = u 0 x , x ∈ R , where λ > 0 , and the linear operator Λ u = ∑ j = 3 5 1 j ∂ x j u.

^{[10]}In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension.

^{[11]}We prove in one space dimension global existence, of positive bounded classical solutions, and establish existence of non-constant equilibrium solutions and assess their stability.

^{[12]}On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

^{[13]}The guiding principle for a rigorous combination is that all parameter types common to more than one space geodetic observation technique should be combined, including their full variance-covariance information as well as the corresponding ties.

^{[14]}Today the remote laboratories are mainly located in one space and use powerful but very expensive hardware and software appliance.

^{[15]}We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap.

^{[16]}Multilingual automatic speech recognition (ASR) system is a single entity capable of transcribing multiple languages sharing a common phone space.

^{[17]}One spacer underwent reresection and the remaining 4 underwent reimplantation with no subsequent infectious complications.

^{[18]}It is derivable by local measurements at multitechnique stations, which operate more than one space geodetic technique.

^{[19]}This study examines how working mothers negotiate her gender role and strategize in facing the condition when domestic and public sphere exist in one space called home after the outbreak COVID-19 pandemic in Indonesia.

^{[20]}The model is the Calogero model, non-relativistic particles interacting with a pair potential $$ \frac{g}{{\left|x-y\right|}^2} $$ g x − y 2 in one dimension, considered as a quantum field theory in one space and one time dimension via the second quantisation.

^{[21]}) which are usually built in large open areas made of simple tent structures, always temporary housing ( The camp) does not include living and sleeping spaces, as well as areas for food preparation, personal hygiene and privacy, but rather one space.

^{[22]}Bone specimens were harvested and processed for histological and histomorphometric analyses to assess new bone formation (N-BF%), remaining bone graft (RBG%) and trabecular bone space (Tb.

^{[23]}In this article, we have investigated anisotropic compact star models threaded by quintessence matter contents in the background of embedded class one spacetime.

^{[24]}Mixed-use development is increasingly popular in land use planning and zoning, fostering a combination of residential, commercial, and cultural uses into one space.

^{[25]}The flux rope is a three-dimensional magnetic structure intrinsically, and it remains unclear whether the composition is uniform along the flux rope axis as most MCs are only detected by one spacecraft.

^{[26]}The article shows the possibility of using Landsat 7 ETM+ multi-zone space imagery and brightness characteristics to predict platinum mineralization in new promising areas.

^{[27]}By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically.

^{[28]}They extract random clusters with arbitrary shapes and positions in one space and evaluate how much the clusters are stretched or dispersed in the other space.

^{[29]}Th) and small bone Trabecular bone space (Tb.

^{[30]}In this work, we designed a novel compound (TPE-Gir) combining a tetraphenylethene aromatic core tethered to four quaternary ammoniums through acylhydrazone spacers, and we investigated in detail its self-assembly and interaction with different types of nucleic acids.

^{[31]}In principle, one space-borne detector, like LISA, could measure the gravitational wave polarizations from a long time observation with its orbital motion.

^{[32]}In this paper we consider a class of diffusive ecological models with two free boundaries and with cross-diffusion and self-diffusion in one space dimension.

^{[33]}In this reflective article, the author proposes that studies of contemporary Scientology would be enriched by a greater emphasis on the notion of ‘Scientologies’ (different types of Scientology across both Church of Scientology and Free Zone spaces).

^{[34]}When viewed as a function from one space to another, neural networks can exhibit feature correlation and slower training due to this redundancy.

^{[35]}If the latter equations are formulated in two dimensions (either one space and one time, or two space dimensions), the UTM expresses the solution in terms of a matrix Riemann–Hilbert (RH) problem with explicit dependence on the independent variables.

^{[36]}We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases.

^{[37]}In this article, we establish scale-invariant Strichartz estimates for the Schrodinger equation on arbitrary compact globally symmetric spaces and some bilinear Strichartz estimates on products of rank-one spaces.

^{[38]}during this paper, OSPF network has one space referred to as (area 0), that has 6-Routers distributed among cities on Iraq’s map.

^{[39]}, the Legendre-Gauss-Lobatto SBP operator in one space dimension.

^{[40]}For a more detailed analysis of airflow and temperature distribution within one space, a computational fluid dynamics (CFD) simulation model was performed.

^{[41]}In more than one space dimension, convex integration techniques developed by De Lellis-Szekelyhidi and Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta.

^{[42]}This is one space worth watching.

^{[43]}We study the $L^2$-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with strictly convex fluxes in one space dimension.

^{[44]}Tone space conversion refers to the conversion or representation of color data in one color space into corresponding data in another color space.

^{[45]}We will use a special Cluster campaign, where one spacecraft was lagged 8 hours behind the three other spacecraft, to obtain near-Earth solar wind measurements upstream of the bow shock, together with simultaneous measurements in the magnetosheath.

^{[46]}In this paper,for a distributive lattice $mathcal L$, we study and compare some lattice theoretic features of $mathcal L$ and topological properties of the Stone spaces ${rm Spec}(mathcal L)$ and ${rm Max}(mathcal L)$ with the corresponding graph theoretical aspects of the zero-divisor graph $Gamma(mathcal L)$.

^{[47]}In this paper, we study superconvergence properties of the local discontinuous Galerkin (LDG) methods for solving nonlinear convection-diffusion equations in one space dimension.

^{[48]}However, a general uniqueness criterion for singular characteristics, not restricted to mechanical systems or problems in one space dimension, is missing at the moment.

^{[49]}In this paper, we study the existence of solutions for a diagonal hyperbolic system, that is not necessarily strictly hyperbolic, in one space dimension, considering discontinuous BV initial data without any restrictions on the size of its norm.

^{[50]}

## Clas One Space

In the present work, we search a new exact solution of Einstein’s field equations using Karmarkar condition of embedded class one space time.^{[1]}In this article, we have investigated anisotropic compact star models threaded by quintessence matter contents in the background of embedded class one spacetime.

^{[2]}For the first time, we present Einstein’s cluster model in embedding class one spacetime.

^{[3]}

## one space dimension

The novelty of the paper is the generalization of already known results in the one space dimension to the multidimensional case.^{[1]}We consider the Cauchy problem for the higher-order nonlinear nonlocal Schrodinger equation in one space dimension i ∂ t u − Λ u = λ u 3 u , t > 0 , x ∈ R , u 0 , x = u 0 x , x ∈ R , where λ > 0 , and the linear operator Λ u = ∑ j = 3 5 1 j ∂ x j u.

^{[2]}In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension.

^{[3]}We prove in one space dimension global existence, of positive bounded classical solutions, and establish existence of non-constant equilibrium solutions and assess their stability.

^{[4]}On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

^{[5]}We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap.

^{[6]}In this paper we consider a class of diffusive ecological models with two free boundaries and with cross-diffusion and self-diffusion in one space dimension.

^{[7]}We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases.

^{[8]}, the Legendre-Gauss-Lobatto SBP operator in one space dimension.

^{[9]}In more than one space dimension, convex integration techniques developed by De Lellis-Szekelyhidi and Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta.

^{[10]}We study the $L^2$-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with strictly convex fluxes in one space dimension.

^{[11]}In this paper, we study superconvergence properties of the local discontinuous Galerkin (LDG) methods for solving nonlinear convection-diffusion equations in one space dimension.

^{[12]}However, a general uniqueness criterion for singular characteristics, not restricted to mechanical systems or problems in one space dimension, is missing at the moment.

^{[13]}In this paper, we study the existence of solutions for a diagonal hyperbolic system, that is not necessarily strictly hyperbolic, in one space dimension, considering discontinuous BV initial data without any restrictions on the size of its norm.

^{[14]}This paper is devoted to the analytical study of the long-time asymptotic behavior of solutions to the Cauchy problem of a system of conservation laws in one space dimension, which is derived from a repulsive chemotaxis model with singular sensitivity and nonlinear chemical production rate.

^{[15]}Our numerical simulations cover the one space dimension case, and two space dimension case with or without spherical symmetry.

^{[16]}We will show that the blow-up rate of any singular solution of (1) is given by the ODE solution associated with ( 1 ) , The result in one space dimension, has been proved in Hamza and Zaag (2020).

^{[17]}We study reflectionless properties at the boundary for the wave equation in one space dimension and time, in terms of a well-known matrix that arises from a simple discretisation of space.

^{[18]}The model accounts for three phases, namely the water, gas, and solid particles (hydrophobic and hydrophilic), in one space dimension.

^{[19]}The similar result for NLS without potential ( V ≡ 0 ), which is invariant of translation and scaling transformation, in one space dimension was obtained by Akahori–Nawa.

^{[20]}This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side.

^{[21]}In this paper, we present and analyze a new space–time ultra-weak discontinuous Galerkin (UWDG) finite element method for the second-order wave equation in one space dimension.

^{[22]}In this paper, we analyze the interaction of localized patterns such as traveling wave solutions for reaction-diffusion systems with nonlocal effect in one space dimension.

^{[23]}We consider the long time behavior of solutions to the initial value problem for the ``complex-valued'' cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension.

^{[24]}In this paper, we develop a family of high order cut discontinuous Galerkin (DG) methods for hyperbolic conservation laws in one space dimension.

^{[25]}Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle $x_i$ with its own jump rate parameter $\nu_i$.

^{[26]}A new method of solution is proposed for the solution of the wave equation in one space dimension with continuously varying coefficients.

^{[27]}The current paper is to investigate the numerical approximation of logistic type chemotaxis models in one space dimension with a free boundary.

^{[28]}This model can be transformed to a local partial differential equation that can be solved numerically easily to generate a reference solution for the IMEX-RK method, but is limited to one space dimension.

^{[29]}Mathematical models that describe these processes and may be employed for simulation, design and control are usually given as nonlinear, time-dependent partial differential equations that in one space dimension include strongly degenerate convection-diffusion-reaction equations with discontinuous coefficients, and in two or more dimensions, coupled flowtransport problems.

^{[30]}We describe and explain a new strategy of discretization of conservation laws, starting from the scalar case in one space dimension, extending it to systems and to the multi-dimensional setting.

^{[31]}Finally, in one space dimension, using the real part of the asymptotic expansion of eigenvalues of the system, we prove that the obtained polynomial decay rate is optimal.

^{[32]}In this paper on hyperbolic systems of conservation laws in one space dimension, we give a complete picture of stability for all solutions to the Riemann problem which contain only extremal shocks.

^{[33]}We prove that the value functions converge to the entropy solution of the master equation, which in this case can be written as a scalar conservation law in one space dimension, and that the optimal trajectories admit a limit: they select one mean field game soution, so there is propagation of chaos.

^{[34]}A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon.

^{[35]}In this paper we investigate a free boundary problem describing S–K–T competition ecological model with two competing species and with cross-diffusion and self-diffusion in one space dimension, where one species is made up of two groups separated by a free boundary, and the other has a single group.

^{[36]}We also study the fully discretized semi-implicit scheme in one space dimension.

^{[37]}

## one space geodetic

The guiding principle for a rigorous combination is that all parameter types common to more than one space geodetic observation technique should be combined, including their full variance-covariance information as well as the corresponding ties.^{[1]}It is derivable by local measurements at multitechnique stations, which operate more than one space geodetic technique.

^{[2]}