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Journal articles on the topic 'Initial space'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Lambour, R., R. Bergemann, C. von Braun, and E. M. Gaposchkin. "Space-Based Visible Space Object Photometry: Initial Results." Journal of Guidance, Control, and Dynamics 23, no. 1 (2000): 159–64. http://dx.doi.org/10.2514/2.4504.

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2

Shamin, R. V. "Spaces of initial data for differential equations in a Hilbert space." Sbornik: Mathematics 194, no. 9 (2003): 1411–26. http://dx.doi.org/10.1070/sm2003v194n09abeh000770.

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3

ELLIS, GEORGE F. R. "THE SPACE OF COSMOLOGICAL SPACE–TIMES." Journal of Hyperbolic Differential Equations 02, no. 02 (2005): 331–79. http://dx.doi.org/10.1142/s0219891605000476.

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I first focus on how to best describe the space of cosmological space–times and what its essential properties are and some comments on the dynamical behavior revealed by studies that will be described in more detail by John Wainwright. I will then relate this both to observations and to anthropic issues (i.e. the possible existence of observers). This space includes some viable singularity free solutions which will be briefly described, thus posing the issue of the tension between very special initial conditions and the existence of initial singularities. I will conclude with remarks on the issue of realized infinities in this context and the concept of multiverses.

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Jain, Amit, Saugat Ray, Rajat Mitra, and S. S. Chopra. "Possibility of space closure without initial alignment." Journal of Indian Orthodontic Society 49, no. 3 (2015): 152–55. http://dx.doi.org/10.4103/0301-5742.165560.

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5

Jayade, Vijay. "Possibility of space closure without initial alignment." Journal of Indian Orthodontic Society 50, no. 2 (2016): 132. http://dx.doi.org/10.4103/0301-5742.179950.

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6

SHARAF, M., A. SAAD, A. SHARAF, and S. NAJMULDEEN. "Space Dynamics with Mathematica. I. Initial Motion." Journal of King Abdulaziz University-Science 16, no. 1 (2004): 89–99. http://dx.doi.org/10.4197/sci.16-1.9.

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7

Jain, Amit, Saugat Ray, Rajat Mitra, and S. S. Chopra. "Possibility of space closure without initial alignment." Journal of Indian Orthodontic Society 49, no. 3 (2015): 152–55. http://dx.doi.org/10.1177/0974909820150306.

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8

Jayade, Vijay. "Possibility of space closure without initial alignment." Journal of Indian Orthodontic Society 50, no. 2 (2016): 132. http://dx.doi.org/10.1177/0974909820160213.

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9

Marshall, Pablo. "STATE SPACE MODELS WITH DIFFUSE INITIAL CONDITIONS." Journal of Time Series Analysis 13, no. 5 (1992): 411–14. http://dx.doi.org/10.1111/j.1467-9892.1992.tb00116.x.

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10

Motro, René. "Teaching of Space Structures with Initial Stresses." International Journal of Space Structures 17, no. 2-3 (2002): 107–16. http://dx.doi.org/10.1260/026635102320321752.

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Teaching of space structures with initial stresses requires an adapted pedagogy. This paper describes some important features of such a teaching, which is delivered for architects, engineers and sometimes artists. The indispensable dialogue between theoretical and experimental methods is underlined. Some characteristics related to the so-called “parametric method” used to understand and design space structures are described. Original pedagogical experiences are presented: bi-cable model, graph theory, formfinding procedure, and construction of prototypes. Teaching of space structures with initial stresses has been mainly included and experimented for more than ten years, both at the University of Montpellier and at the School of Architecture, in academic courses the contents of which are presented.

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11

Tesfahun, Achenef. "Almost critical local well-posedness for the space-time monopole equation in Lorenz gauge." Communications in Contemporary Mathematics 17, no. 03 (2015): 1450043. http://dx.doi.org/10.1142/s0219199714500436.

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Recently, Candy and Bournaveas proved local well-posedness of the space-time monopole equation in Lorenz gauge for initial data in Hs with [Formula: see text]. The equation is L2-critical, and hence a [Formula: see text] derivative gap is left between their result and the scaling prediction. In this paper, we consider initial data in the Fourier–Lebesgue space [Formula: see text] for 1 < p ≤ 2 which coincides with Hs when p = 2 but scales like lower regularity Sobolev spaces for 1 < p < 2. In particular, we will see that as p → 1+, the critical exponent [Formula: see text], in which case [Formula: see text] is the critical space. We shall prove almost optimal local well-posedness to the space-time monopole equation in Lorenz gauge with initial data in the aforementioned spaces that correspond to p close to 1.

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12

Yakar, Coşkun. "Initial Time Difference Quasilinearization Method in Banach Space." Communications in Mathematics and Applications 2, no. 2&3 (2011): 77–85. http://dx.doi.org/10.26713/cma.v2i2-3.133.

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13

Liu, Shengyi, and Roger A. Dougal. "Initial velocity effect on space‐charge‐limited currents." Journal of Applied Physics 78, no. 10 (1995): 5919–25. http://dx.doi.org/10.1063/1.360593.

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14

Boyd, Patricia T., and Stephen L. W. McMillan. "Initial-value space structure in irregular gravitational scattering." Physical Review A 46, no. 10 (1992): 6277–87. http://dx.doi.org/10.1103/physreva.46.6277.

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15

Takenawa, T., M. Eguchi, B. Grammaticos, Y. Ohta, A. Ramani, and J. Satsuma. "The space of initial conditions for linearizable mappings." Nonlinearity 16, no. 2 (2003): 457–77. http://dx.doi.org/10.1088/0951-7715/16/2/306.

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16

Stumbles, S. "The initial value problem for radiating space-times." Annals of Physics 169, no. 1 (1986): 220–42. http://dx.doi.org/10.1016/0003-4916(86)90165-x.

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17

Sharples, Jason. "Local existence of quasispherical space–time initial data." Journal of Mathematical Physics 46, no. 5 (2005): 052501. http://dx.doi.org/10.1063/1.1864250.

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18

Cunningham, Carson F., Kent L. Gee, Grant W. Hart, et al. "Initial findings from Space Launch System liftoff measurements." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A71. http://dx.doi.org/10.1121/10.0018198.

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This presentation documents initial findings from far-field noise measurements at NASA’s Kennedy Space Center during liftoff of the Space Launch System’s Artemis I mission, which occurred on November 16, 2022. The vehicle— the most powerful ever successfully launched into orbit—consists of four liquid-fueled RS-25 engines and two five-segment, solid-fuel rocket boosters (SRBs). Because this was the first launch, the noise radiation characteristics of this vehicle were previously unknown. Overall sound pressure levels, waveform characteristics, and spectra are described at distances ranging from 1.5 to 8.4 km. The levels due to the SRBs’ ignition overpressure are particularly intense in the direction of the flame trench exit. The post-liftoff maximum one-third octave spectrum has a peak at 20 Hz, and maximum overall levels are greater than described in a pre-launch environmental assessment. These and other findings presently submitted to JASA Express Letters further understanding of super heavy-lift rocket acoustics.

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19

Demir, İzzettin, Bedre Özbakır, and İsmet Yıldız. "A contribution to the study of soft proximity spaces." Filomat 31, no. 7 (2017): 2023–34. http://dx.doi.org/10.2298/fil1707023d.

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In this paper we study the soft proximity spaces. First, we investigate the relation between proximity spaces and soft proximity spaces. Also, we define the notion of a soft ?-neighborhood in the soft proximity spaces which offer an alternative approach to the study of soft proximity spaces. Later, we show how a soft proximity space is derived from a soft uniform space. Finally, we obtain the initial soft proximity space determined by a family of soft proximity spaces.

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20

R. Maheswari and K. Rekha. "INITIAL GRILL NANO TOPOLOGICAL SPACES WITH INITIAL GRILL NANO GENERALIZED CLOSED SETS." jnanabha 54, no. 02 (2024): 76–82. https://doi.org/10.58250/jnanabha.2024.54206.

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The main objective of this paper is to introduce an initial grill Nano - topological space and investigate the types of initial grill Nano - open sets. Also, we introduce an initial grill Nano generalized closed set and study its fundamental properties

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21

Jin, Hong Sung, Minkyu Kwak, and Bataa Lkhagvasuren. "Stability result for the surface quasi-geostropic equations with horizontal dissipation in anisotropic Sobolev space." Journal of Mathematical Physics 63, no. 9 (2022): 091507. http://dx.doi.org/10.1063/5.0087229.

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The stability of smooth solutions of an anisotropic surface quasi-geostrophic equation with horizontal dissipation remains an open problem. In this work, we present a partial answer to this problem in a rougher function space. More precisely, if the initial data θ0 belong to anisotropic Sobolev space H0, s with [Formula: see text], then there exists a global small solution, provided that the initial data are small in H0, s. The stability problem in the space H0,1 or more regular spaces remains open. The main tools used are the Littlewood–Paley theory and standard techniques.

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22

Ghaforyan, Hossein, Somayyeh Shoorvazi, Alireza Sepehri, and Tooraj Ghaffary. "More on extracting information about the initial state from the black hole radiation." Modern Physics Letters A 33, no. 19 (2018): 1850108. http://dx.doi.org/10.1142/s0217732318501080.

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Recently, some authors showed that a classical collapse scenario ignores this richness of information in the resulting spectrum and a consistent quantum treatment of the entire collapse process might allow us to retrieve much more information from the spectrum of the final radiation. We confirm these results and show that by considering the quantum entanglement between metrics, we can uncover information of black holes. In our model, a density matrix is defined for the spaces, both inside and outside of the event horizon. These inside and outside spaces of black holes are obtained by tracing from a bigger space. An observer that lives in this big space can recover total information regarding the inside and outside of black hole.

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23

Prenov, Rahat. "The positivity of the differential operator generated by hyperbolic system of equations." e-Journal of Analysis and Applied Mathematics 2023 (December 31, 2023): 54–63. http://dx.doi.org/10.62780/ejaam/2023-005.

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In the present paper, the initial value problem for the hyperbolic system of equations with nonlocal boundary conditions is investigated. The positivity of the space operator generated by the given problem in interpolation spaces is established. The structure of interpolation spaces of this differential operator is studied. The positivity of this space operator in Slobodeckij-Sobolev spaces is established.

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24

Guo Lingling, 郭玲玲, 汪少林 Wang Shaolin, 代海山 Dai Haishan та ін. "天基光学监测空间碎片初始轨道确定". Acta Optica Sinica 44, № 24 (2024): 2412002. http://dx.doi.org/10.3788/aos240738.

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25

Krasnoschok, M. V. "Solvability in Holder Space of an Initial Boundary Value Problem for the Time-Fractional Diffusion." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 1 (2016): 48–77. http://dx.doi.org/10.15407/mag12.01.048.

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26

Alonso-Mallo, I., and C. Palencia. "On the convolution operators arising in the study of abstract initial boundary value problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 3 (1996): 515–39. http://dx.doi.org/10.1017/s0308210500022897.

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We consider convolution operators arising in the study of abstract initial boundary value problems. These operators are of the formwhere {S(t)}t ≧0 is a C0-semigroup in a Banach space X,, with infinitesimal generator A0,: D(A0), ⊂ X, → X, and K(z): Y → X is a linxear, continuous mapping defined in another Banach space Y., We study the continuity of T between the spaces Lp([0, + ∞), Y), and Lq([0, + ∞), X), 1 ≦ p, q, ≦ + ∞. We give several examples of the applicability of the results to some familiar initial boundary value problems, including both parabolic and hyperbolic cases.

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27

Shimada, Yuta, Yuki Tashiro, Kiyotaka Izumi, Koichi Yoshida, and Takeshi Tsujimura. "Initial alignment method for free space optics laser beam." Japanese Journal of Applied Physics 55, no. 8S3 (2016): 08RB08. http://dx.doi.org/10.7567/jjap.55.08rb08.

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28

Kecker, Thomas. "Space of initial conditions for a cubic Hamiltonian system." Complex Variables and Elliptic Equations 64, no. 1 (2018): 132–42. http://dx.doi.org/10.1080/17476933.2017.1423479.

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29

Redouane-Salah, E., and C. W. Bauer. "Monte Carlo phase space integration for initial state radiation." Journal of Physics: Conference Series 1525 (April 2020): 012003. http://dx.doi.org/10.1088/1742-6596/1525/1/012003.

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30

Li, Lin, Qiu-Zhi Qu, Bin Wang, et al. "Initial Tests of a Rubidium Space Cold Atom Clock." Chinese Physics Letters 33, no. 6 (2016): 063201. http://dx.doi.org/10.1088/0256-307x/33/6/063201.

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31

Forbes, Kevin F., and O. C. St. Cyr. "Space weather and the electricity market: An initial assessment." Space Weather 2, no. 10 (2004): n/a. http://dx.doi.org/10.1029/2003sw000005.

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32

Kung, J. H., and Robert H. Brandenberger. "Chaotic inflation as an attractor in initial-condition space." Physical Review D 42, no. 4 (1990): 1008–15. http://dx.doi.org/10.1103/physrevd.42.1008.

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33

Pereira, R., and P. Rocha. "Feasible initial conditions for 2D discrete state-space systems." IFAC-PapersOnLine 55, no. 30 (2022): 127–31. http://dx.doi.org/10.1016/j.ifacol.2022.11.040.

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34

Shields, Jackson, Oscar Pizarro, and Stefan Williams. "Feature Space Exploration For Planning Initial Benthic AUV Surveys." Field Robotics 3, no. 1 (2023): 652–86. http://dx.doi.org/10.55417/fr.2023021.

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Special-purpose Autonomous Underwater Vehicles (AUVs) are utilized for benthic (seafloor) surveys, where the vehicle collects optical imagery of the seafloor. Due to the small-sensor footprint of the cameras and the vast areas to be surveyed, these AUVs can not feasibly collect full coverage imagery of areas larger than a few tens of thousands of square meters. Therefore it is necessary for AUV paths to sample the surveys areas sparsely, yet effectively. Broad-scale acoustic bathymetric data are readily available over large areas and are often a useful prior of seafloor cover. As such, prior bathymetry can be used to guide AUV data collection. This research proposes methods for planning initial AUV surveys that efficiently explore a feature space representation of the bathymetry, in order to sample from a diverse set of bathymetric terrain. This will enable the AUV to visit areas that likely contain unique habitats and are representative of the entire survey site. We propose several information gathering planners that utilize a feature space exploration reward, to plan freeform paths or to optimize the placement of a survey template. The suitability of these methods to plan AUV surveys is evaluated based on the coverage of the feature space and also the ability to visit all classes of benthic habitat on the initial dive. Informative planners based on Rapidly expanding Random Trees (RRT) and Monte Carlo Tree Search (MCTS) were found to be the most effective. This is a valuable tool for AUV surveys as it increases the utility of initial dives. It also delivers a comprehensive training set to learn the relationship between acoustic bathymetry and visually derived seafloor classifications.

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35

Saha, Anup, and Sandip Das. "The effect of a hypocycloid irregularity on torsional surface waves in a multilayer system." Theoretical and Applied Mechanics, no. 00 (2024): 7. http://dx.doi.org/10.2298/tam240112007s.

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The present topic is devoted to investigating the effects of semi four-cusped hypocycloid irregularity on torsional surface waves in an initially stressed anisotropic porous medium situated between two anisotropic nonhomogeneous semi-infinite spaces. The irregularity manifests as a semi-fourcusped hypocycloid at the interface where the layer and the lower semi-infinite space are separated. It is assumed that the directional rigidities, density and initial stress vary in the upper and lower semi-infinite spaces in an exponential and hyperbolic manner, respectively. A closed form for the torsional wave dispersion equation is presented. Additionally, the velocity equation is found in the case of no irregularity. The study demonstrates that heterogeneity of lower semi-infinite space, initial stress and directional rigidities of both semiinfinite spaces, as well as of porosity of the layer have a favourable effect on the phase velocity of torsional surface waves. However, the heterogeneity of the upper semi-infinite space, ratio of directional rigidities and initial stress of the layer and irregularity parameter have a negative impact. It has also been observed that, in the case of a uniform media, the velocity equation reduces to the conventional equation for the Love wave.

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36

Yin, Yewen, Zhenwei Li, Chengzhi Liu, Zhe Kang, Jiannan Sun, and Long Chen. "Improved Initial Orbit Determination Based on the Gooding Method of Low Earth Orbit Space Debris Using Space-Based Observations." Remote Sensing 15, no. 21 (2023): 5217. http://dx.doi.org/10.3390/rs15215217.

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Initial orbit determination (IOD), as a basis for initial orbit association and accurate orbit determination (OD), has a crucial role in the process of obtaining space debris orbit information. Among the traditional methods, the Gooding method has better convergence and stability. In this study, the Gooding method is enhanced to solve the issues discovered. A novel initial orbit determination (IOD) method is developed using the proposed improvement measures of the single-parameter initial value determination (SIVD) method, the fitted-curve noise suppression method, the restricted corrective value solution method, the removal of trivial solutions, etc. The experimental results verify the effectiveness of the improved method. The success rate of the initial orbit determination reached 99%, and the accuracy of the solved orbit parameters was significantly improved, especially the semi-major axis (SMA) error of less than 50 km, accounting for 88% of the total. It can be seen that the method meets the demand of space-based space debris cataloging for initial orbit association and can serve in the field of space situational awareness, which has important practical significance and application potential.

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37

Malygina, Vera, and Kirill Chudinov. "ON ASYMPTOTIC PROPERTIES OF THE CAUCHY FUNCTION FOR AUTONOMOUS FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE." Applied Mathematics and Control Sciences, no. 3 (October 5, 2020): 7–26. http://dx.doi.org/10.15593/2499-9873/2020.3.01.

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We investigate stability of a linear autonomous functional differential equation of neutral type. The basis of the study is the well-known explicit solution representation formula including an integral operator, the kernel of which is called the Cauchy function of the equation under study. It is shown that the definitions of Lyapunov, asymptotic and exponential stabilities can be formulated without loss of generality in terms of the corresponding properties of the Cauchy function. The conclusion is drawn that stability with respect to initial data depends on the functional space which the initial function belongs to, and, as a consequence, that there is the need to indicate this space in the definition of stability. It is shown that, along with the concept of asymptotic stability, a certain stronger property should be introduced, which we call strong asymptotic stability. The main study is devoted to stability with respect to initial function from spaces of integrable functions. Special attention is paid to the study of asymptotic and exponential stability. We use the following known properties of the Cauchy function of an equation of neutral type: this function is piecewise continuous, and its jumps are determined by a Cauchy problem for a linear difference equation. We obtain that the strong asymptotic stability of the equation under consideration for initial data from the space L1 is equivalent to an exponential estimate of the Cauchy function and; moreover, we show that these properties are equivalent to the exponential stability with respect to initial data from the spaces Lp for all p from 1 to infinity inclusive. However, we show that strong asymptotic stability with respect to the initial data from the space Lp for p greater than one may not coincide with exponential stability.

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38

Antoine, Jean-Pierre, and Camillo Trapani. "PIP-Space Valued Reproducing Pairs of Measurable Functions." Axioms 8, no. 2 (2019): 52. http://dx.doi.org/10.3390/axioms8020052.

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We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space Z : = Z ( X , μ ) , where ( X , μ ) is a measure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbert spaces; (ii) Y is a Hilbert space, but Z is a pip-space; (iii) Y and Z are both pip-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space Y. Examples are presented for each case.

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39

Wang, Ying, Ji-lin Zhou, Fu-yao Liu, Wei Sun, Hui-Gen Liu, and Ming Yang. "The influence of inclinations on the dynamical stability of multi-planet systems." Monthly Notices of the Royal Astronomical Society 490, no. 1 (2019): 359–70. http://dx.doi.org/10.1093/mnras/stz2375.

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ABSTRACT A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.

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40

Holmén, Janne. "Time and Space in Time and Space." Contributions to the History of Concepts 15, no. 2 (2020): 105–29. http://dx.doi.org/10.3167/choc.2020.150206.

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Mental maps and historical consciousness, which describe the spatial and temporal dimensions of worldviews, are not, as commonly stated, twentieth century concepts. Historical consciousness was coined simultaneously by several German scholars in the mid-1800s. Mental maps, used in English since the 1820s, had a prominent role in US geography education from the 1880s. Since then, the concepts have traveled between practical-technical, educational, and academic vocabularies, cross fertilizing fields and contributing to the formation of new research questions. However, when these initial periods of reflection gave way to empirical investigation, strict intra-disciplinary definitions of the concepts have strengthened disciplinary borders by excluding the interpretations of the same concepts in other fields.

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41

Blömker, Dirk, Giuseppe Cannizzaro, and Marco Romito. "Random initial conditions for semi-linear PDEs." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (2019): 1533–65. http://dx.doi.org/10.1017/prm.2018.157.

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AbstractWe analyse the effect of random initial conditions on the local well-posedness of semi-linear PDEs, to investigate to what extent recent ideas on singular stochastic PDEs can prove useful in this framework.In particular, in some cases, stochastic initial conditions extend the validity of the fixed-point argument to larger spaces than deterministic initial conditions would allow, but in general, it is never possible to go beyond the threshold that is predicted by critical scaling, as in our general class of equations we are not exploiting any special structure present in the equation.We also give a specific example where the level of regularity for the fixed-point argument reached by random initial conditions is not yet critical, but it is already sharp in the sense that we find infinitely many random initial conditions of slightly lower regularity, where there is no solution at all. Thus criticality cannot be reached even by random initial conditions.The existence and uniqueness in a critical space is always delicate, but we can consider the Burgers equation in logarithmically sub-critical spaces, where existence and uniqueness hold, and again random initial conditions allow to extend the validity to spaces of lower regularity which are still logarithmically sub-critical.

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42

Radomirskaya, K. A. "Matching Spectral and Initial-Boundary Value Problems." Contemporary Mathematics. Fundamental Directions 63, no. 2 (2017): 316–39. http://dx.doi.org/10.22363/2413-3639-2017-63-2-316-339.

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Based on the approach to abstract matching boundary-value problems introduced in [18], we consider matching spectral problems for one and two domains. We study in detail the arising operator pencil with self-adjoint operator coeﬃcients. This pencil acts in a Hilbert space and depends on two parameters. Both possible cases are considered, where one parameter is spectral and the other is ﬁxed, and properties of solutions are obtained depending on this. Also we study initial-boundary value problems of mathematical physics generating matching problems. We prove theorems on unique solvability of a strong solution ranging in the corresponding Hilbert space.

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43

Qadomi, Ala, Maysam Abu-Dalu, Saud Al-Sadi, and Hamed M. Obiedat. "Application of the dual space of Gelfand-Shilov spaces of Beurling type." Boletim da Sociedade Paranaense de Matemática 40 (February 6, 2022): 1–7. http://dx.doi.org/10.5269/bspm.50603.

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Using a previously obtained structure theorem of Gelfand-Shilov spaces $\Sigma _{\alpha }^{\beta }$ of Beurling type of ultradistributions, we prove that these ultradistributions can be represented as an initial values of solutions of the heat equation by describing the action of the Gauss-Weierstrass semigroup on the dual space $(\Sigma _{\alpha }^{\beta})^{\prime }.$

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44

Zhou, Xuhuan, and Weiliang Xiao. "Algebra Properties in Fourier-Besov Spaces and Their Applications." Journal of Function Spaces 2018 (December 4, 2018): 1–10. http://dx.doi.org/10.1155/2018/3629179.

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We estimate the norm of the product of two scale functions in Fourier-Besov spaces. As applications of these algebra properties, we establish the global well-posedness for small initial data and local well-posedness for large initial data of the generalized Navier-Stokes equations. Particularly, we give a blow-up criterion of the solutions in Fourier-Besov spaces as well as a space analyticity of Gevrey regularity.

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Gorodetskiy, V., R. Kolisnyk, and O. Martynyuk. "ON A NONLOCAL PROBLEM FOR PARTIAL DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE." Bukovinian Mathematical Journal 8, no. 2 (2020): 24–39. http://dx.doi.org/10.31861/bmj2020.02.03.

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Spaces of $S$ type, introduced by I.Gelfand and G.Shilov, as well as spaces of type $S'$, topologically conjugate with them, are natural sets of the initial data of the Cauchy problem for broad classes of equations with partial derivatives of finite and infinite orders, in which the solutions are integer functions over spatial variables. Functions from spaces of $S$ type on the real axis together with all their derivatives at $|x|\to \infty$ decrease faster than $\exp\{-a|x|^{1/\alpha}\}$, $\alpha > 0$, $a > 0$, $x\in \mathbb{R}$. The paper investigates a nonlocal multipoint by time problem for equations with partial derivatives of parabolic type in the case when the initial condition is given in a certain space of generalized functions of the ultradistribution type ($S'$ type). Moreover, results close to the Cauchy problem known in theory for such equations with an initial condition in the corresponding spaces of generalized functions of $S'$ type were obtained. The properties of the fundamental solution of a nonlocal multipoint by time problem are investigated, the correct solvability of the problem is proved, the image of the solution in the form of a convolution of the fundamental solution with the initial generalized function, which is an element of the space of generalized functions of $S'$ type.

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Li, Jing, Bing-Yu Zhang, and Zhixiong Zhang. "A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 43. http://dx.doi.org/10.1051/cocv/2019027.

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This paper studies the initial boundary value problem (IBVP) for the dispersive Kuramoto-Sivashinsky equation posed in a finite interval (0, L) with non-homogeneous boundary conditions. It is shown that the IBVP is globally well-posed in the space Hs(0, L) for any s > −2 with the initial data in Hs(0, L) and the boundary value data belonging to some appropriate spaces. In addition, the IBVP is demonstrated to be ill-posed in the space Hs(0, L) for any s < −2 in the sense that the corresponding solution map fails to be in C2.

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Hu, Yi. "An Initial Exploration of the Development Mode of Characteristic Towns." Academic Journal of Management and Social Sciences 4, no. 3 (2023): 22–25. http://dx.doi.org/10.54097/ajmss.v4i3.12454.

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Characteristic towns have a unique geographic space, cultural space and industrial space, and is an important platform for promoting the integrated development of urban and rural areas, as well as an important opportunity for industrial restructuring and upgrading, and our country now has a solid foundation for building characteristic towns. The article succinctly elucidates the concept, characteristics, and formation paths of characteristic towns, and analyzes the development mode of characteristic towns in Shaanxi Province, and puts forward suggestions for promoting the development mode of characteristic towns in Shaanxi Province.

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Zanuik, Tomaž. "Feudalisation of open public space." Maska 39, no. 219 (2024): 14–27. http://dx.doi.org/10.1386/maska_00182_1.

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“Privatisation happens in many ways. [...] The fundamental characteristic of public space – its universal accessibility for all – is endangered by increasing control and surveillance.”I Social segregation also contributes to feudalisation, which is another attack on public space. Although no one is talking about it yet, the initial casualties of this feudalisation – due to increased restrictions and costs for accessing public spaces that must be purchased – will not only be fire brigades and other organisers of commercial and entertainment events, including festivities, but also, similar to the scarcity of production spaces, producers of cultural noise or non-profit events in the realm of independent and non-governmental arts and culture.

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Martinez, Ginelle M. "A Call for Space-domain Intelligence Training." Journal of Advanced Military Studies 15, no. 1 (2024): 88–100. http://dx.doi.org/10.21140/mcuj.20231501005.

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U.S. Space Force intelligence initial skills training (IST) currently occurs via U.S. Air Force pipelines. However, as the Space Force matures, it must take ownership of its training programs. Consolidating guardian intelligence initial skills training under the purview of the newest Service fosters a critical space-domain focused mindset and guardian culture at the outset of a member’s career.

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Laur, Henri. "Envisat — Initial results." Space Research Today 162 (April 2005): 31–35. http://dx.doi.org/10.1016/s0045-8732(05)80017-8.

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