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Prestressed concrete is generally used in constructions with long spans or large rooms without columns, such as halls, sports halls, meeting rooms, etc. Large column-free rooms in buildings require long-span beam structures to maximize space functions. This research was conducted on an 8-story building with long-span beam structures on floors 6, 7, and 8 using pre-stressed concrete as an alternative to reinforced concrete. This research aims to obtain beam dimensions regarding structural response and internal forces. The research results obtained prestressed beam dimensions of 0.9 x 0.55m and reinforced concrete beam dimensions of 1.2 x 0.8m. The results of the structural response analysis showed that the deviation of the prestressed beam is greater than the structure using reinforced concrete beams; the internal forces and deflections also decreased after using beam structures with prestressed concrete. From these results, it can be concluded that prestressed concrete can be used in long-span beam structures. [ABSTRACT FROM AUTHOR]

The results of a study of the problem of assessing the environment-forming functions of green spaces in the city of Hrodna which is a large multifunctional settlement are presented. The contribution of green spaces to the formation of the gas composition of the atmosphere (carbon deposition) and thermal pollution of the urban environment is estimated. It was determined that the low volume of carbon deposition (less than 100 t/year) is typical for urban landscapes with industrial, mixed industrial and communal storage buildings and reaches 3500-5500 t/year in complexes confined to the valleys of the Neman and Lasosna rivers. The assessment of the level of intensity of thermal radiation showed that high indicators are associated with urban landscapes with complex buildings – apartment, urban-type manor, public, industrial, low levels were noted within the Neman valley and the Pogorany-Koshevniki district, where the proportion of green areas is high. The relationship between the levels of carbon dioxide deposition and the average surface temperature of Hrodna has been found, that confirms the necessity of considering the structure of urban landscapes when assessing the environmental functions of their green spaces. [ABSTRACT FROM AUTHOR]

With the advancement of knowledge technology, the library building has evolved to cater for more than just a space to read and learn. It has become a space for working, social interaction, community activity and more. With this growing trend to accommodate this demand for more functionality, the library design needs to adapt to this growth to bring the best experience to the occupants. Biophilic design is a fitting approach to help enhance the occupants' experience with these evolving functions of the library spaces. The biophilic design employs a variety of innovative ways to be implemented in a space varying from the literal introduction of nature, symbolic representation, the essence of the space and more, to create a space that encourages a sense of connection with nature. This study aims to examine various biophilic designs used in library spaces from selected case studies with known biophilic design applications in the spaces and assesses the importance of these biophilic designs to the occupants based on their perception. The findings show that most of the library occupants agreed that biophilic design is an essential aspect of the space in the library with visual connection with nature and prospect to be of utmost importance based on the survey conducted. [ABSTRACT FROM AUTHOR]

The purpose of this work is to present the concept of best one-sided approximation of unbounded functions in weighted space by using algebraic operators in connection of average modulus for smoothness type. More precisely, we demonstrate the existing of some algebraic operators for single-directional approximation of unbounded functions in the terms of average modulus of smoothness. We also show that, the direct theorems to approximate unbounded functions in weighted space by one-sided approximation methods. [ABSTRACT FROM AUTHOR]

The main areas of application of various spaces of generalized functions lie in the theory of differential equations and in the theory of quadrature and cubature formulas. Therefore, there is a need to study the spaces of generalized functions, connected with various domains in Rn. Modern formulation of the problem of optimization of approximate integration formulas consists in minimizing the norm of the error functional formula on chosen normed spaces. Since in this paper we consider the space of functions defined on the n- dimensional torus Tn, i.e. on a manifold that is not a Euclidean space (we assume that the Euclidean structure is locally maintained), it is necessary to discuss the question of the invariance of the introduced norm under orthogonal transformations. The difficulties that arise are related to the fact that the space of periodic functions on Rn is not invariant under rotations. The space of derivatives of m order at point x forms m symmetric power of the introduced tangent space and is denoted by S(T)m. It is required that the introduced norm at each point be invariant under orthogonal transformations of tangent space T (x). [ABSTRACT FROM AUTHOR]

In this paper, we consider the construction of an optimal lattice quadrature formula in the space W 2 (m) (0, 1). Further, finding the extremal function of the error functional of quadrature formulas, by virtue of the Riesz theorem on the general form of a linear continuous functional, is reduced to solving a boundary value problem for ordinary differential equations. Solving this boundary value problem, we obtain an explicit expression for the extremal function of the error functional of quadrature formulas. In addition, by virtue of the Riesz theorem, the square of the norm of the error functional is explicitly calculated and an analytical expression is obtained for the optimal coefficients of the quadrature formulas at m = 2. [ABSTRACT FROM AUTHOR]

In the present paper optimal quadrature formula for approximate evaluation of Fourier coefficients is constructed for functions of the space K2(Pm)(0, 1). At the same time explicit formulas for the optimal quadrature formulas are obtained. The obtained formula is exact for the trigonometric functions sin ωx, cos ωx and for polynomials of degree m− 3. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing optimal difference formulas for an approximate solution to the Cauchy problem in the Sobolev space of functions of the m-th order derivatives (in the generalized sense) are square integrable. Using a discrete analogue of a differential operator of the first order, one can find representations of optimal difference formulas. In the first section, we consider the construction of optimal explicit difference formulas of the Adams type. Here, minimizing the norm of the error functional with respect to the coefficients, a system of linear algebraic equations is obtained. This system is reduced to a system of convolution equations. And it is completely solved using a discrete analogue of a second-order differential operator. In the second section, an optimal implicit difference formula in the Sobolev space is constructed. In the remaining sections, the square of the norm of the error functional of optimal explicit and implicit difference formulas is calculated in the dual Sobolev space. Analysis of the work shows that implicit formulas give better convergence than explicit ones. [ABSTRACT FROM AUTHOR]

In the monographs of S.L. Sobolev and Kh.M. Shadimetov proved that the rectangle formula is an optimal quadrature formula in the Sobolev space of periodic functions. In addition, it is shown there that the error of the constructed optimal quadrature formula is estimated in terms of the step of the quadrature formula and Bernoulli numbers. The subject of this work is the construction of an optimal composite quadrature formula, i.e. quadrature formula involving the values of the derivatives of the function being integrated. Here we propose a new method for constructing composite optimal quadrature formulas based on the periodization of an arbitrary function from the Sobolev space of non-periodic functions and optimal quadrature formulas for rectangles. [ABSTRACT FROM AUTHOR]

In this paper, in the space L 2 (2) (0, 1) - the space of functions whose second-order generalized derivative is summed with a square on the interval [0, 1], we consider the construction of a weighted optimal lattice quadrature formula with derivatives. We are further finding the extremal function of the error functional of quadrature formulas, constructing optimal quadrature formulas with first-order derivatives, and obtaining analytical expressions for the coefficients of these weighted optimal quadrature formulas with first-order derivatives. [ABSTRACT FROM AUTHOR]

In the numerical solution of Initial Value Problems (IVP) for ordinary differential equations, computational methods serve to approximate the determination of functions representing the solution of these problems. The problem of finding the most convenient numerical expressions for a function and its connection with methods for improving such approximations plays an important role in practical calculations. It is of great interest to consider the so-called discrete methods, i.e. methods that determine the solution for discrete values of the independent variable. Discrete methods are currently the most widely used. One of the discrete methods is difference formulas for the numerical solution of the IVP. In this paper, in the Sobolev space where all derivatives up to the mth order participate in the norms of functions, we consider the problem of constructing optimal difference formulas. In the optimization of difference formulas, i.e. when constructing optimal difference formulas in function spaces, an important role is played by the extremal function of a given difference formula. In this paper, the extremal function of the difference formula is explicitly found in the Sobolev space. Next, the square of the norm of the error functional of difference formulas is calculated. Minimizing this norm with respect to the coefficients of the difference formulas, a system of equations is obtained. In addition, the existence and uniqueness of a solution to the resulting system are proved. [ABSTRACT FROM AUTHOR]

In this article, the optimal quadrature formula construction is elucidated for numerical integration of the right Riemann-Liouville integral in the Hilbert space of real-valued functions. Firstly, the norm of the error functional is found using the extremal function of the error functional of the quadrature formula. Since the error functional is illustrated on the Hilbert space, the quadrature formula that we are constructing is exact for zero element of the space. That is, we have the conditions that the influence of the error functional on these functions is equal to zero. Then, the Lagrange function is constructed to find the conditional extremum of the error functional. Thereby, a linear equations system is gained for the coefficients of the optimal quadrature formula. The existence and uniqueness of the solution of the obtained system are analyzed. [ABSTRACT FROM AUTHOR]

This paper uses the Ritz method to find approximate solutions to boundary-value problems for ordinary differential equations. We present the approximate finite element solution by a linear combination of the basis functions. Here we get co-efficients of the optimal interpolation formula in W 2 (1 , 0) space as basis functions. The difference obtained in numerical results and exact solutions illustrates graphically. [ABSTRACT FROM AUTHOR]

There are several methods for constructing optimal quadrature formulas, such as the spline method, the ϕ-function method, and the Sobolev method, which is based on the use of discrete analogues of differential operators. In this paper, we study the optimization of quadrature formulas in the space of functions that have generalized third-order derivatives that are square summable. Here, the norm of functions is introduced using special parameters. In the space under consideration, using the extremal function of the error functional of quadrature formulas and a discrete analog of the sixth-order differential operator, optimal quadrature formulas will be constructed. [ABSTRACT FROM AUTHOR]

In this paper, it is considered the problem of integral geometry in three-dimensional space over a family of cones with a weight function of a special form. The theorem of existence and uniqueness of the solution is proved and an explicit formula for the solution is obtained. [ABSTRACT FROM AUTHOR]

There are several methods for constructing optimal quadrature formulas, such as the spline method, the ϕ-function method, and the Sobolev method, which is based on the use of discrete analogues of differential operators. In this paper, we study the optimization of quadrature formulas in the space of functions that have generalized third-order derivatives that are square summable. Here, the norm of functions is introduced using special parameters. In the space under consideration, using the extremal function of the error functional of quadrature formulas and a discrete analog of the sixth-order differential operator, optimal quadrature formulas will be constructed. [ABSTRACT FROM AUTHOR]

We design and investigate an infinite first order 3-system of differential equations in Hilbert space l2. We prove the existence and continuity of a unique solution of the system by showing the solution belongs to the space of continuous functions in l2 on some finite time interval. [ABSTRACT FROM AUTHOR]

In this work, the statement and proof of a fundamental formula in the phase space representation of quantum systems will be carried out for the similitude group, Sim(2). This formula takes the form ∫ a(Y)P(Y)d(Y) = 〈Â〉, where Y is the phase space variable and 〈Â〉 is a linear operator on Hilbert space representing a quantum dynamical observable. 〈Â〉 is the quantum expected value of the observable in a state of the system. The focus on the similitude group is due to current interest in signal analysis, localization operators and pseudo-differential operators. The fundamental formula states that this may be computed in a classical manner, as an integral against a probability distribution. The formula is intimately related to the quantization-dequantization problem a(Y) ⟷ Â which assigns a quantum operator to the classical phase space function a(Y). [ABSTRACT FROM AUTHOR]

A space of functions is associated with differential operator if the operator transforms the space into itself. This paper shows the construction of all first-order operators with complex coefficients that are associated with the meta-anti-analytic function space. Such construction was possible by obtaining necessary and sufficient conditions on the coefficients of the first order complex differential operator. Application of this research is aimed to find solutions to initials values problems involving space and operators associated with each other. [ABSTRACT FROM AUTHOR]

Let ℱ be a given differential operator acting with respect to spacelike variables, then a function space ℬ is called an associated space to ℱ if ℱ applies ℬ into itself. In this research work, a characterization of all the first-order differential operators with coefficients in the Clifford algebra CLn that are associated to the space of solution functions of the partial differential equation Δ ˜ = d i v (B ∇) u = 0 has been determined. To make this possible the equation Δ ˜ u = 0 and some special solutions of such equation were used. The results found imply that the technique of associated spaces allows to solve certain initial value problems. [ABSTRACT FROM AUTHOR]

Using Schwarz's lemma, we give an estimation of the schlicht radius for normalized functions in the closed unit ball of Bloch-type spaces. As consequences of our results, we obtain distortion-type theorems for normalized µ-Bloch functions and we prove that for certain classes of functions in ℬµ, the norm is obtained by taking supremum over f-1(Σε) = {z ∈ ℂ: |arg(z)| < ε}. [ABSTRACT FROM AUTHOR]

Robotics is among the much-touted treatment and therapy solutions in modern dentistry. A unique Particle Swarm Optimization PSO is utilized to manage the needle tip location and direction as a function of the knots along the path between the end-effector segments in a dentistry robotics navigation system recently suggested. The innovative "Numeric Alphabet Flow" (NAF) method may control any point-to-point surgical motions for a three-link robotic guiding system. The new NAF approach creates a brand-new form known as the NAF-PSO methodology by using flowing values and alphanumeric characters in the fuzzy rules and employing particle swarm optimization techniques. Within that paper, we use the novel NAF-PSO to improve robotic tracking performance. This study introduces a unique route planner that specifies the suggested NAF-PSO function as minimizing space and traveling time while not reaching a maximal preset force and avoiding obstacles. [ABSTRACT FROM AUTHOR]

The notion of grill was employed in this work to generalize a new form of compact space and investigate its features, as well as its link to previously established concepts, as well as the definition of new categories of functions such as lindeloff space and determining the relationship between them, this set will be a beginning point for investigating the numerous futures of this set by offering many instances and attributes that pertain to it. [ABSTRACT FROM AUTHOR]

The objective of this work is studied approximation d-monotone unbounded function in weighted space by using some types of algebraic polynomials of degree ≤ d − 1 which interpolates a d-monotone function f and d knot, sufficiently approximations it, even if the knot of interpolation are close to each other moreover, we are establish the degree of approximation of d-monotone mappings in collection Lp,w(x), 1 ≤ p < ∞ in terms modulus of smoothness and the average modulus of smoothness τd weighted space. [ABSTRACT FROM AUTHOR]

The objective of this work is studied approximation d-monotone unbounded function in weighted space by using some types of algebraic polynomials of degree ≤ d − 1 which interpolates a d-monotone function f and d knot, sufficiently approximations it, even if the knot of interpolation are close to each other moreover, we are establish the degree of approximation of d-monotone mappings in collection Lp,w(x), 1 ≤ p < ∞ in terms modulus of smoothness and the average modulus of smoothness τd weighted space. [ABSTRACT FROM AUTHOR]

A time-dependent removal model for air pollutants from an elevated source is considered. It leads to solving numerically linear inverse problem for a space degenerate ultraparabolic equation with unknown time-dependent right hand side. The feature of such problems are special integral overdetermination conditions. We use the fractional step method of N. N. Yanenko to split the problem into two subproblems: diffusion and advection step. To overcome the vertical degeneration we perform the space discretization of the parabolic subproblem by fitted finite volume method. For solving of the inverse problem we use solution decomposition with respect to unknown source. Numerical experiments demonstrate the efficiency of our method. We also discuss how the present results can be used for solving inverse problems of ultraparabolic equations having two or three unknown time and space functions in their right hand sides. [ABSTRACT FROM AUTHOR]

Public spaces, as elements of the city's structure and a reflection of its history, are images of city life and indicate a character of the city. Shaped in accordance with an urban concept and functions, they determine the identity of the city and become city-forming factors. City squares, an example of public places, are a forum showing urban and architectural changes taking place in the city by giving them a specific form and function in a changing reality. Piastowski Square in Bydgoszcz is a space with a given, endogenous and commercial function. For over 150 years, this area, despite changes in the concept of development, has retained its architectural and urban structure and importance for this part of the city. As a place bringing together commercial and service activities of citizens, as well as having features and objects characteristic of the heritage of this place, it has preserved and still maintains the local identity of the urban space. The aim of this article is to trace how the square changed functionally over the decades but still maintained its original urban layout and to indicate the factors that allowed the character and distinctiveness of this space to be maintained in a dynamically changing reality. The method of work is based on a comparative analysis of selected, similar squares in Poland, iconographic materials and in situ research. The main conclusions indicate that despite the functional, architectural and urban transformations of the square, from its foundation in the mid-nineteenth century to the present day, it was possible to create a spatially and socially valuable area. The preserved space and function of the square's retail trade and services still have a positive effect and enliven this part of the city's downtown area. From its beginning, the space of the square is invariably connected with the spatial system of Bydgoszcz through a clear urban layout, communication and greenery. Treated as a peripheral area for years and thus degraded, it is now regaining its importance for the city's identity and is partially revitalized. The role of historical urban public spaces in the global world is to shape urban landscape in such a way that it retains its distinctiveness, reflects local history and individuality also on a local scale. A stable functional program and the contributing architecture allow to preserve the most valuable elements of the city, and renew the valuable urban fabric. The architectural and urban heritage, such as the area of Piastowski Square, skilfully fits in the contemporary needs of the citizens, and at the same time strengthens and creates an interesting, unique shape of the urban space, recommended in many contemporary scientific studies. [ABSTRACT FROM AUTHOR]

In this paper we study convergence and summability problems of the series associated with the Laplace-Beltrami operator on the unique sphere. These series known as Fourier-Laplace series and we study the behaviour of these series in the different spaces of smooth functions with respect number of topologies. [ABSTRACT FROM AUTHOR]

In this paper, in the space W 2 (m) (0, 1) (this is the space of functions, the m-th generalized derivative of which is integrable with a square in the interval [0, 1]) we consider the construction of an optimal lattice quadrature formula. Finding the extremal function of the error functional of quadrature formulas, by virtue of the Riesz representation theorem, is reduced to solving a boundary value problem for ordinary differential equations. By solving this boundary value problem, an explicit expression for the extremal function of the quadrature formulas is obtained. In addition, in the Sobolev space W 2 (m) (0, 1) the square of the norm of the error functional of quadrature formulas is explicitly calculated. We obtain a number of interesting and new results that are unattainable in the classical sense. Some theorems are presented and established in [1] theoretically support computational simplifications that reduce costs. [ABSTRACT FROM AUTHOR]

S.L. Sobolev [1] firstly posed the problem of finding an extremal function for an interpolation formula and calculating the norm of the error functional in the space W 2 m . In this paper, an extremal function of the interpolation formula was found in explicit form in the Sobolev space W 2 m , functions for which the generalized derivatives of order m are square integrable. In the present paper, we consider the problem of finding the norm of the error functional for interposional formulas of Hermite type in the space of S.L. Sobolev W ˜ 2 (m) (T1). [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing optimal difference formulas for approximate solution to the Cauchy problem in the Hilbert space of functions which are square integrable with second-order derivatives. Using the discrete analogue of the second-order differential operator we find representations of optimal difference formulas. [ABSTRACT FROM AUTHOR]

In this paper the concept of intuitionistic fuzzy Completely generalized #α-continuous functions and intuitionistic fuzzy almost generalized #α-continuous functions have been introduced and explore its properties. [ABSTRACT FROM AUTHOR]