Norm Function Research Articles

К вопросу об определении места градостроительного права в системе права России

A relevant and controversial aspect in the modern theory of law in the development of the modern doctrine of the legal system is the question of the intersectoral division of the Russian legal system, the criteria for its construction, as well as the isolation and systematization of legal norms that are complex in nature. The purpose of the article is to establish intersectoral connections, criteria for systematization and the place in the system of Russian law of urban planning norms as a legal community that combines elements of private law and public law influence in the mechanism of legal regulation. A systematic approach and such logical research methods as analysis and synthesis made it possible to determine the place of urban planning norms in the system of Russian law as an independent branch of law with a special mixed type of legal regulation. Scope of application of the results: the main results and conclusions of the study can be used as the basis for the formation of new approaches to building a legal system and criteria for differentiating legal norms. In addition, the recognition of urban planning law as an independent branch of law will significantly facilitate the processes of law enforcement and law-making activities in the urban planning industry. Conclusions: the totality of the subject, method, principles, goals and functions of urban planning norms, forming a special mechanism of legal regulation, indicates the qualitative originality of the regulated sphere of social relations and the isolation of urban planning law as part of the Russian legal system as a branch of law. At the same time, the complex nature of urban planning law by type of legal regulation is due to the interpenetration of private law and public law interests.

Defining the functions of administrative law norms in the modern theory of administrative law

Defining the functions of administrative law norms in the modern theory of administrative law

Relating Quartz Crystallographic Preferred Orientation Intensity to Finite Strain Magnitude in the Northern Snake Range Metamorphic Core Complex, Nevada: A New Tool for Characterizing Strain Patterns in Ductilely Sheared Rocks

AbstractDocumenting the magnitude of finite strain within ductile shear zones is critical for understanding lithospheric deformation. However, pervasive recrystallization within shear zones often destroys the deformed markers from which strain can be measured. Intensity parameters calculated from quartz crystallographic preferred orientation (CPO) distributions have been interpreted as proxies for the relative strain magnitude within shear zones, but thus far have not been calibrated to absolute strain magnitude. Here, we present equations that quantify the relationship between CPO intensity parameters (cylindricity and density norm) and finite strain magnitude, which we calculate by integrating quartz CPO analyses (n = 87) with strain ellipsoids from stretched detrital quartz clasts (n = 49) and macro‐scale ductile thinning measurements (n = 7) from the footwall of the Northern Snake Range décollement (NSRD) in Nevada. The NSRD footwall exhibits a strain gradient, with Rs(XZ) values increasing from 5.4 ± 1.4 to 282 ± 122 eastward across the range. Cylindricity increases from 0.52 to 0.83 as Rs increases from 5.4 to 23.5, and increases gradually to 0.92 at Rs values between 160 and 404. Density norm increases from 1.68 to 2.97 as Rs increases from 5.4 to 23.5, but stays approximately constant until Rs values between 160 and 404. We present equations that express average finite strain as a function of average cylindricity and density norm, which provide a broadly applicable tool for estimating the first‐order finite strain magnitude within any shear zone from which quartz CPO intensity can be measured. To demonstrate their utility, we apply our equations to published data from Himalayan shear zones and a Cordilleran core complex.

Grundnorm and Grounding A modern Metaphysics for Hans Kelsen’s Pure Theory?

Abstract This article explores the possibility of reconstructing Hans Kelsen’s neo-Kantian theory of the basic norm (Grundnorm) with the help of the theory of (metaphysical) grounding. First, we outline Kelsen’s theory of the basic norm as an integral part of his neo-Kantian transcendental idealism and give a sketch of grounding theory; we then try to fit these theories together. As it turns out, grounding theory has some internal flaws. More importantly, several of the features of a metaphysical ground are not compatible with the roles which Kelsen ascribes to the basic norm – its roles as a keystone of the legal hierarchy and as a transcendental-logical condition of legal cognition. Finally, an alternative conception is examined, according to which the legal system is grounded not by the basic norm but by social facts, with the basic norm serving as a bridging principle. However, this alternative is flawed as well; its main problem seems to be that it violates the dualism of ‘Is’ and ‘Ought’. The argument is relevant for the concept of personhood, because Kelsen treats the term ‘person’ in law as a mere expression for the unity of a specific set of legal norms, so that the identity of persons is ultimately dependent on the identity and function of the basic norm of the legal system.

On the Economic Origins of Concerns over Women’s Chastity

Abstract This paper studies the origins and function of customs and norms that intend to keep women from being promiscuous. Using large-scale survey data from more than 100 countries, I test the anthropological theory that a particular form of preindustrial subsistence – pastoralism – favored the adoption of such customs and norms. Pastoralism was characterized by frequent and often extended periods of male absence from the settlement, implying difficulties in monitoring women’s behavior and larger incentives to imposing restrictions on women’s promiscuity. The paper shows that women from historically more pastoral societies (i) are subject to stronger anti-abortion attitudes; (ii) aremore likely to have undergone infibulation, the most invasive form of female genital cutting; (iii) are more restricted in their freedom of mobility; and (iv) adhere to more restrictive norms about women’s promiscuity. At the historical society level, pastoralism predicts patrilocality, the custom of living close to the husband’s family after marriage, allowing them to monitor the bride. Instrumental variable estimations that make use of the ecological determinants of pastoralism support a causal interpretation of the results. I also provide evidence that the mechanism behind these patterns is male absence, rather than male dominance, per se, or historical economic development.

Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space (lq(·)(Lp(·))). Moreover, it was developed using classical Lebesgue space (Lp) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not.

Tensor double arc-tangent norm minimization for multi-view clustering

Tensor structures are widely utilized in clustering tasks due to their ability to represent high-order relationships among multi-view data. The rank and decomposition of tensors are essential characteristics that have recently received considerable attention. Most approaches approximate tensor rank using the tensor nuclear norm (TNN) and non-convex rank functions. We introduce a multi-view clustering method based on an enhanced self-expression with a tensor double arc-tangent norm. Initially leveraging tensor singular value decomposition, this method impartially approximates the true rank of the tensor, avoiding rank overestimation. The enhanced self-expression further utilizes the latent connections among the original data. Then, we propose an improved alternating direction method of multipliers (ADMM) for rapid optimization of the model. Experiments conducted on six datasets confirm the effectiveness of the proposed model.

Cubic Structure on Soft Gamma-m-Normed Linear Space

Objectives: The purpose of this research is to take the lead in comprehending the fuzzy idea of cubic structure on soft Gamma-m normed linear space. According to the theory of Soft m-Normed Linear Space (SMNLS), we offer the conviction of Cauchy's sequence and convergence in cubic Soft Gamma-m Normed Linear Space (CSGMNLS). We have obtained certain results like the concept of completeness in CSGMNLS. Methods: In this paper we defined the soft gamma ring, soft gamma ideals and soft gamma vector space which are used to introduce the notion of soft gamma-2-normed linear space, Soft Gamma-m-Normed Linear Space (SGMNLS) and its properties. Also, the CSGMNLS can be analyzed by using the SGMNLS. Findings: In this research from CSGMNLS construct a norm function that satisfies the properties of SGMNLS, and additionally given that example with proof in which a sequence is cauchy sequence and convergence in SGMNLS if it is cauchy and convergence sequence in CSGMNLS. Also, provided theorem and its proof for completeness of a sequence in CSGMNLS. Novelty: Already gamma ring and fuzzy n-normed linear space has been defined. We introduced the concept of SGMNLS using this also initiated the CSGMNLS and some results obtained from its properties. We suggested a necessary conditions for completeness of a sequence in CSGMNLS. Keywords: Soft Gamma ring, Soft gamma vector space, Soft gamma normed linear space, Soft m-norm, Soft m-normed linear space, 2-Normed and m-normed right soft gamma linear space

Optimal Design of Formulas for a Single Degree of Freedom Tuned Mass Damper Parameter Using a Genetic Algorithm and H2 Norm.

One of the researchers' concerns in structural engineering is to control the dynamic behavior of structures efficiently. The TMD (tuned mass damper) is one of the effective methods of controlling the vibration of structures, and various numerical techniques have been proposed to find the optimal parameters of the TMD. This paper develops a new explicit formula to derive the optimal parameters of the TMD of a single degree of freedom (SDOF) structure under seismic load using a genetic algorithm (GA). In addition, the state-space model and the H2 norm function are used to identify the optimal frequency ratio and damping ratio of the TMD that minimize the overall vibration energy of the structure. The MATLAB curve fitting toolbox is used for the explicit formula proposal, and the validity of the proposed formula is verified through multidimensional performance verification technique. Finally, the TMD parameters of the SDOF structure are applied to the multi-degrees of freedom (MDOF) structure to compare and analyze with the existing research results, and the results of the explicit formula proposed in this paper are confirmed to be excellent. This paper can suggest a new direction for determining the optimal TMD parameters using a GA and can be effectively applied to vibration control problems of various structures.

WELL-TO-WELL (W2W) ELECTROMAGNETIC TOMOGRAPHY MODELING ADVANCEMENT: IMPROVING PRECISION AND EFFECTIVENESS WITH REGULARIZATION

This research describes the direct and inverse problems of cross-well electromagnetic tomography. The model geometry has azimuthal symmetry, which simplifies the forward modeling and the inversion procedure. In the direct problem, the finite element method is used in the numerical solution of the Helmholtz equation. In the inverse problem, the study discusses the use of three stabilizer functionals: Global Smoothness (GS), Total Variation (TV), and Absolute Equality (AE). The first uses a smoothing function in the L2 norm, while the latter uses smoothing in the L1 norm, for it accepts abrupt changes between adjacent parameters. The results show that the TV method generated good estimates of both geometry and conductivity of the bodies, both for small and large conductivity contrast between the targets and the surrounding environment. Through the results, one can also observe that the regularization of the Total Variation presented a better estimate of the parameters than the Global Smoothness. In most of the synthetic models used in this work, the best estimates of the proposed model occurred when Absolute Equality constraints were used on the cells at the edges of the inversion grid, in addition to the stabilizer functional.

Application of locally regularized extremal shift to the problem of realization of a prescribed motion

Abstract A controlled system of differential equations under the action of an unknown disturbance is considered. The problem discussed in the paper consists in constructing algorithms for forming a control that provides the realization of a prescribed motion for any admissible disturbance. Namely these algorithms should provide the closeness in the metric of the space of differentiable functions of a phase trajectory of a given controlled system and some etalon trajectory of an analogous system functioning when any outer actions are absent. As the space of admissible disturbances, we take the space of measurable square integrable (with respect to the Euclidean norm) functions. The cases of inaccurate measurements of phase trajectories of both systems at all times and at discrete times are under study. Two computer oriented algorithms for solving the problem are designed. The algorithms are based on the (well-known in the theory of guaranteed control) method of extremal shift. In the process, its local (at each time of control correction) regularization is performed by the method of smoothing functional (the Tikhonov method). In addition, estimates for algorithm’s convergence rate are presented.

Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions

Let H∞ be the Banach algebra of bounded analytic functions on the unit open disc D equipped with the supremum norm. As well known, inner functions play an important role in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define Qinn and Qout the maps from H∞ to I the set of inner functions and F the set of outer functions, respectively. In this paper, we study the H2-norm continuity and H∞-norm discontinuity of Qinn and Qout on some subsets of H∞. On the other hand, the Beurling theorem connects inner functions and invariant subspaces of the multiplication operator Mz. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of Qinn and Qout on Hol(D‾), the set of all analytic functions in the closed unit disk, are considered. In addition, we also study the factor maps Q[inn] and Q[out] from H∞ to I/T and F/T, where I/T is the quotient space of I mod T and F/T is the quotient space of F mod T.

Convergence of matrix transform means with respect to the Walsh–Kaczmarz system

Abstract In this paper the Walsh system will be considered in the Kaczmarz rearrangement. We estimate the difference between matrix transform means of Walsh–Kaczmarz–Fourier series and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also prove norm convergence with similar conditions.

Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations

We consider a class of second order elliptic equations in divergence form with non-uniform exponential degeneracy. The method used is based on the fact that the degeneracy rates of the eigenvalues of the matrix ||aij(x)|| (function λi(x)) are not the functions of unusual norm |x|, but of some anisotropic distance |x| a−. We assume that the Dirichlet problem for such equations is solvable in the classical sense for every continuous boundary function in any normal domain Ω. Estimates for the weak solutions of Dirichlet problem near the boundary point are obtained, and Green’s functions for second order non-uniformly degenerate elliptic equations are constructed.

Genetic analysis of phenotypic indicators for heat tolerance in crossbred dairy cattle

Climate change-induced rise in global temperatures has intensified heat stress on dairy cattle and is contributing to the generally observed low milk productivity. Selective breeding aimed at enhancing animals’ ability to withstand rising temperatures while maintaining optimal performance is crucial for ensuring future access to dairy products. However, phenotypic indicators of heat tolerance are yet to be effectively factored into the objectives of most selective breeding programs. This study investigated the response of milk production to changing heat load as an indication of heat tolerance and the influence of calving season on this response in multibreed dairy cattle performing in three agroecological zones Kenya. First-parity 7-day average milk yield (65 261 milk records) of 1 739 cows were analyzed. Based on routinely recorded weather data that were accessible online, the Temperature-Humidity Index (THI) was calculated and used as a measure of heat load. THI measurements used represented averages of the same 7-day periods corresponding to each 7-day average milk record. Random regression models, including reaction norm functions, were fitted to derive two resilience indicators: slope of the reaction norm (Slope) and its absolute value (Absolute), reflecting changes in milk yield in response to the varying heat loads (THI 50 and THI 80). The genetic parameters of these indicators were estimated, and their associations with average test-day milk yield were examined. There were no substantial differences in the pattern of milk yield response to heat load between cows calving in dry and wet seasons. Animals with ≤50% Bos taurus genes were the most thermotolerant at extremely high heat load levels. Animals performing in semi-arid environments exhibited the highest heat tolerance capacity. Heritability estimates for these indicators ranged from 0.06 to 0.33 and were mostly significantly different from zero (P < 0.05). Slope at THI 80 had high (0.64–0.71) negative correlations with average daily milk yield, revealing that high-producing cows are more vulnerable to heat stress and vice versa. A high (0.63–0.74) positive correlation was observed between Absolute and average milk yield at THI 80. This implied that low milk-producing cows have a more stable milk production under heat-stress conditions and vice versa. The study demonstrated that the slope of the reaction norms and its absolute value can effectively measure the resilience of crossbred dairy cattle to varying heat load conditions. The implications of these findings are valuable in improving the heat tolerance of livestock species through genetic selection.

Variations of Peace in Colombia

ABSTRACT Peace and conflict are not the same across territories and scales. Conceptualizing peace, as a process based on three core functions of society and related norms – provision of security, participation and conflict transformation – allows us to identify variations in peacebuilding needs and perceptions. Methodologically, the article first develops a conceptual framework and then tests it with a case study of Colombia – a subnationally diverse country with a long history of violence and peacebuilding. The entanglement of different scales shapes the diversity of peace and highlights the opportunities and challenges of peacebuilding and related norms, along with their diffusion and contestation.

Morphing from the TV-Norm to the l 0 -Norm.

For piecewise constant objects, the images can be reconstructed with under-sampled measurements. The gradient image of a piecewise image is sparse. If a sparse solution is a desired solution, an -norm minimization method is effective to solve an under-determined system. However, the -norm is not differentiable, and it is not straightforward to minimize an -norm. This paper suggests a function that is like the -norm function, and we refer to this function as meta -norm. The subdifferential of the meta -norm has a simple explicit expression. Thus, it is straightforward to derive a gradient descent algorithm to enforce the sparseness in the solution. In fact, the proposed meta norm is a transition that varies between the TV-norm and the -norm. As an application, this paper uses the proposed meta -norm for few-view tomography. Computer simulation results indicate that the proposed meta -norm effectively guides the image reconstruction algorithm to a piecewise constant solution. It is not clear whether the TV-norm or the -norm is more effective in producing a sparse solution. Index Terms-Inverse problem, optimization, total-variation minimization, -norm minimization, few-view tomography, iterative algorithm, image reconstruction.

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

AbstractIn this article, we provide a systematic and constructive way to build a Lyapunov–Krasovskii functional for time‐delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov–Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input‐to‐state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE‐PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.

EXTRAPOLATION IN SOME MIXED-NORMED FUNCTION SPACES

Abstract. From the beginning of this century non-standard function spaces attracted a considerable attention of researchers. One of such spaces is variable exponent Lebesgue space (Nakano space) 𝐿𝑝(.); another one is grand Lebesgue space 𝐿𝑝0). The main reason to study these spaces was to solve a number of contemporary problems arising naturally in Applied Mathematics and PDEs (see, e.g., [1-5]). Mixed norm function spaces play an important role in Harmonic Analysis and PDEs (see, e.g. the survey by L. Huang and D. Yang (2019), papers by N. V. Krylov.

Modeling the concept of “environment”

In the science of law legal definitions are considered as the semantic core, thanks to which a legal norm functions, and represent a reliable legal basis for further social transformations. In order to identify the characteristic features, properties, content of the concept of environment and its components, to establish their relationship, features of legal effect, the common, scientific and legal meanings of the definitions were compared. The methodological basis of the study was general scientific (analysis, synthesis, generalization) and special legal methods (formal logical, legal modeling method). Modeling the conceptual framework of the ecological legislation in Russia is not only of scientific but also of practical interest. It enables to identify the characteristic features, properties of the concept of environment, the relationship among its elements as a potential subject of further research contributing to in-depth study, identification of gaps and improvement of legislation. The legal model of environment contains a schematic and descriptive part, demonstrating the concept, system and its content, thanks to which environmental legal norms function that reflect the essence of legal regulation and state policy of Russia in the field of environmental protection and the use of natural resources, clearly shows its shortcomings and determines the directions to improve legislation.