General Expression Research Articles

Generality and Exception in Islamic Legal Theory: Intent, Language, and the Jurist’s Role

Abstract Whenever discussions arise about the generality or specificity of law and legal provisions, they occur on at least two different levels. On the external level, there is an expectation that law should be general insofar as similar cases and factual situations are concerned, and specific with regards to different and exceptional cases. This is often invoked as a requirement for what constitutes good law or proper governance. On the internal level, generality refers to the expectation that law must offer coherent rules, principles, or standards of action in some form. General and specific language (al-ʿām wal-khāṣṣ) in Islamic legal theory (uṣūl al-fiqh) enjoyed a noteworthy degree of attention in modern scholarship. This attention largely centers on those concepts’ external potential for driving reform in specific areas of law. This Article, by contrast, focuses on the generality–specificity binary as a tool for ensuring the law’s internal cohesiveness, including its claims to legitimacy and its enforceability. To this end, the Article offers an overview of the examination of general and specific expressions in the thought of two influential twelfth-century C.E. (sixth-centuryA.H.) jurist-theologians of different juristic and theological affiliation: the Shāfiʿī-Ashʿarī Abū Ḥāmid al-Ghazālī (d. 1111 C.E./505 A.H.) and the Central Asian Ḥanafī-Māturīdī ʿAlāʾ al-Dīn al-Samarqandī (d. 1145 C.E./539 A.H.). The Article then goes on to argue that ensuring a coherent relation between intent, language, and norms was a central guiding purpose of these studies. We can see this with particular clarity in the fact that, despite reaching comparable practical positions concerning how norms ought to follow from general language, each jurist attained his conclusion through a different path, reflecting different understandings of the relation of norms to divine intent.

A closed-form expression derived from virtual testing for structural optimization of L-flange bolted connections

L-flange bolted joints are extensively used in different industrial sectors, such as wind turbine towers, rocket stages, or pipelines. Typically, the design of these connections is based on analytical expressions derived from simplified beam models. However, the influence of specific factors such as curvature, adjacent bolts, or joint separation are not addressed within conventional approaches. Finite element models offer the advantage of comprehensively accounting for these effects and the interaction between different failure mechanisms. Nevertheless, their industrial implementation requires significant computational resources, in contrast to the use of analytical formulae. In this context, this paper proposes a new framework for designing optimized L-flange bolted connections, based on general closed-form expressions that rely on validated numerical results. Three expressions, each one related to a particular failure mechanism, are derived from parametric simulations varying the most influencing parameters in the structural behavior. The generated equations can be easily implemented to guide the design process towards an optimal configuration, taking advantage of beneficial effects not addressed within classical approaches. A closer prediction of the actual load capacity of the joint can be obtained, providing a tool that allows engineers to make more reliable and economical designs.

Fear and Public Safety From the Baumanian Perspective

Objective: The aim is to analyze, in view of baumanian ideas, the fear and public insecurity that affect the Brazilian population in the post-modern era, particularly in recent decades, a phenomenon present in the fluid society, which propagates uncertainty and determines the way of thinking, acting and feelings of individuals. Theoretical Framework: Zygmunt Bauman developed research into the complex web that involves individuals' personal and social ties, in which he produced studies on fear and (in)security, as well as coining the generic expression liquid life, characterized by a precarious routine, with uncertainty, devoid of of a defined and stable model, resembling a liquid. Method: A theoretical, critical and dialectical methodological research, of a bibliographic nature, is carried out, based on a qualitative study, in which a deductive model is used, in light of the contributions of the polish professor. Results and Discussion: It is hoped to provoke a level of discussion that leads to understanding and solutions regarding certain conflicts that exist in the social fabric, such as fear and insecurity that affect citizens. Research Implications: El tema investigado está lleno de interés público, porque involucra y afecta al Estado y a todos los segmentos de la sociedad; por lo tanto, no se pueden ignorar sus causas, efectos y consecuencias. Originality/Value: The approach used in the research is authentic and original, because there is no specific production on fear and Brazilian net public security, categories that impact the lives of citizens, which justifies the study of matters that affect cultural, political and social development from the country.

Shear-free inhomogeneous energy density in 4D Einstein-Gauss-Bonnet spherical systems

We explore the inhomogeneity factors for the initially regular relativistic spheres in 4D-Einstein-Gauss-Bonnet (EGB) theory. The corresponding equations of motion are derived once the generic expressions for the kinematical variables are obtained for spherically symmetric self-gravitating system. By using the non-zero divergence of the stress-energy tensor, the independent components of Bianchi identities are constructed. To enable a thorough explanation of the inhomogeneity of the particular shear free matter distribution, we computed two distinct components of evolution equations employing the Weyl tensor. We then investigate the requisite variables for the irregularity by looking at particular scenarios in both the adiabatic and non-adiabatic domains. These instances demonstrate how, in addition to other factors, the Gauss-Bonnet terms contribute to the regularity requirements of the collapsing fluid.

Quantum nature of spacetime near the black hole singularity

The concept of spacetime loses its usual interpretation at the essential singularity of a black hole. In consequence, all laws of physics must fail at this classical singularity. This unphysical behavior of spacetime at the singularity originates from general relativity. In order to have a consistent description of spacetime, this singularity must disappear in a quantum mechanical description of spacetime which is expected to be given by a quantum theory of gravity. In this paper, we therefore attempt to describe the quantum nature of spacetime in the vicinity of the (classical) singularity of a black hole. We take the Kantowsi–Sachs representation for the interior spacetime of a black hole and include inevitable vacuum fluctuations of matter field in the Klein–Gordon representation. Hence we obtain the Wheeler–DeWitt equation for the black hole interior and solve this equation exactly yielding a general expression for the interior wave function of the black hole. Admissible wave functions consistent with the DeWitt boundary condition implies that the Hilbert space has three nonoverlapping sectors distinguished by the relative character of the eigenvalues. Regular quantum black holes with admissible and well-behaved wave function having no singularity can exist only in two of those sectors. However, the remaining sector does not contain any regular quantum black hole.

Interfacial waves in a piezoelectric/piezomagnetic/piezoelectric structure with magneto-electro-mechanical imperfect interfaces

In this paper, we study the propagation of Shear Horizontal (SH) waves in the interfaces of a piezoelectric/piezomagnetic/piezoelectric (PiezoE/ PiezoM/ PiezoE) structure with a magnetical, imperfect magnetic, electric, and mechanical condition at interfaces. The inclusion of magnetical imperfections produced several new results, such as a general dispersion relation and expressions for some limit cases, which were not reported previously in the literature, predicting the existence of interfacial waves. Employing numerical calculations, dispersion curves for this kind of structure are presented for the first time. It can be shown that the magnetical imperfection interface influences the dispersion curves. Our results show that especially magnetic imperfections have a significant influence on the dispersion curves.

Tilted-Plane Structure of the Energy of Finite Quantum Systems.

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.

Interaction of Hermite–Gaussian Beams with a Macroscopic Atomic Target

AbstractA theoretical analysis is presented on the photoexcitation of a macroscopic atomic target by a Hermite–Gaussian (HG) beam within the framework of density matrix theory. Special emphasis is paid to the influence of the incoming HG mode on the population of an excited state and the emitted fluorescence radiation. In particular, a general expression for the alignment parameter of the excited state is derived, which depends on the beam parameters of the HG mode. Although the developed theory can be applied to any atomic system, here the electric dipole transition in neutral sodium atoms is investigated when driven by three , and modes. For this optical (valence‐shell) excitation, it is demonstrated that the population of the excited state is sensitive to the beam waist and the mode index of the HG beam. Furthermore, the influence of beam parameters on the angular distribution and linear polarization of the emitted fluorescence radiation is discussed.

Study of the large bending behavior of CNTs using LDTM and nonlocal elasticity theory

The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.

A shock-tube experimental and kinetic simulation study on the autoignition of methane at ultra-lean and lean conditions

Coalbed methane represents an important kind of natural gas resource in many countries. However, the low-concentration property of coalbed methane limits its applications. To gain insight into the combustion kinetics of coalbed methane and facilitate its combustion utilization, this work reports an experimental and kinetic simulation study on the autoignition properties of methane at ultra-lean and lean conditions. A shock-tube (ST) facility is used for ignition delay time (IDT) measurements with equivalence ratios at 0.5, 0.1, and 0.05 with pressure at 2 and 10 bar under the temperature ranging from 1320 to 1850 K. The measured IDTs can be correlated into a general Arrhenius expression, and the equivalence ratio effect on IDTs is then analyzed. Seven detailed chemical kinetic mechanisms are employed to predict the IDTs and statistical error indicators are used to evaluate their performance. Detailed kinetic analysis via sensitivity and reaction path analysis is performed to uncover the kinetic differences among the seven mechanisms. It is shown that some of the reaction paths only exist in the NUIGMech1.3 mechanism, while the other detailed mechanisms do not consider them. Reaction path analysis indicates that the reactions related to O2, OH and O species become more important compared to the reactions involving CH3 and H radicals as the equivalence ratio decreases from lean to ultra-lean conditions. Detailed chemical kinetics analysis is also conducted to demonstrate the uncertainty of key reactions. The present work should be valuable to gain insight into the methane ignition characteristics and to facilitate kinetic mechanism optimization of methane combustion.

Simplified Universal Equations for Ionic Conductivity and Transference Number

Nernst-Einstein equation can provide a reasonable estimate of the ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green–Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman’s treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to simplified, ready-to-use expressions of conductivity and transference numbers that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general analytical expressions for conductivity and transference number are simplified for binary electrolytes, and numerical solutions are provided for ternary and quaternary mixtures with ion dissociation.

Dynamic modeling and analysis of multi-flexible-link space manipulators under time-varying dynamic boundary conditions

This paper presents a dynamic modeling method for the multi-flexible-link space manipulators under time-varying dynamic boundary conditions. This method is based on 3D recursive kinematics and is applicable to the space manipulators with an arbitrary number of flexible links. The elastic deflection of the flexible links is described by using the Assumed Mode Method (AMM). The general expressions of the dynamic boundary conditions are derived by combining the Newton-Euler equation with 3D recursive kinematics. Based on 3D recursive kinematics, the dynamic model suitable for space manipulators with an arbitrary number of flexible links is established. For the multi-flexible-link manipulator systems, the movement of the links will alter the mass distribution of the system, resulting in the time-varying modes of the links. The difference between the results of the time-varying modes and time-invariant modes are investigated. Numerical simulations are performed to verify the adaptability of the proposed dynamic modeling method to different manipulators. Simulation results shows that the results of time-varying modes are in good agreement with those of time-invariant modes, and the simulation calculation time of time-invariant modes is less than that of time-varying modes. For the above reasons, the time-invariant modes are sufficient and it is unnecessary to update the modes.

Investigating Magnetohydrodynamic Motions of Oldroyd-B Fluids through a Circular Cylinder Filled with Porous Medium

We analytically investigated the magnetohydrodynamic motions of electrically conductive, incompressible Oldroyd-B fluids through an infinite circular cylinder filled with a porous medium. A general expression was established for the dimensionless velocity of fluid as a cylinder moves along its symmetry axis with an arbitrary velocity; the expression can generate exact solutions for any motion of this fluid type, solving the discussed problem. Special cases were considered and validated through graphical investigation to illustrate important characteristics of fluid behavior. In application, this is the first presentation of an exact general expression for non-trivial shear stress related to the magnetohydrodynamic motions of Oldroyd-B fluids when a longitudinal time-dependent shear stress is applied to the fluid by a cylinder. Solutions for the motions of rate-type fluids are lacking. The graphical representations show that in the presence of a magnetic field or porous medium, fluids flow more slowly and the steady state is reached earlier.

Teaching old laws new tricks: Specific energy requirements for breakage based on modern kernels and a population balance model

A general expression for specific energy requirements in particle breakage is derived from a population balance model. The model employs power-law rate kernels, self-similar fragment distributions and an energy dependence based on the Vogel-Peukert master curve. This model connects the empirical constants and exponents of size in older empirical energy laws to the parameters of the population balance model, the nature of the particles, and certain moments of the self-similar particle size distribution predicted by the model. The resulting model is used to extract values of the order of the power-law rate kernel from literature data. The extracted order values are consistent with known expressions for individual particle breakage. The model developed here may be coupled with experimental determination of the material parameter needed in the Vogel-Peukert master curve to enable extraction of energy utilization efficiency values from experimentally determined values of the size-independent portion of the selection function.

Vapor pressure to Boltzmann distribution law connection and its empirical corrections

Vapor pressure (P) data of pure substances in gas/solid-liquid equilibrium is important for scientific research and practical applications. Due to the large temperature range going from melting point to critical point, it is an impossible task to determine the P of a pure substance at each temperature point. Up to now, there is no general equation that can accurately describe the relation between temperature (T) and P for all pure substances. Utilizing Boltzmann distribution, we presented a general expression, ln P = a + bT + cln(T) + d(1/T), for the P of pure substances, that is, the P-T dependence is nearly exponential over the entire range of liquid and solid existence. Furthermore, on the base of above equation, we established a corrected general equation to express the liquid vapor pressure within temperature in going from melting point to critical point.lnP=a+bT+cTT/Tb+d(ln(T))+f(ln(T))T/Tb+g(1/T)The results show that the corrected equation has the advantages of universality, simplicity, and high calculation accuracy for the vapor pressure involving liquid simple substances, liquid inorganic and liquid organic compounds.

Central limit theorem for intrinsic Fréchet means in smooth compact Riemannian manifolds

We prove a central limit theorem (CLT) for the Fréchet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Fréchet mean is unique. Previous general CLT results in this setting have assumed that the cut locus of the Fréchet mean lies outside the support of the population distribution. In this paper we present a CLT under some mild technical conditions on the manifold plus the following assumption on the population distribution: in a neighbourhood of the cut locus of the population Fréchet mean, the population distribution is absolutely continuous with respect to the volume measure on the manifold and in this neighhbourhood the Radon–Nikodym derivative has a version that is continuous. So far as we are aware, the CLT given here is the first which allows the cut locus to have co-dimension one or two when it is included in the support of the distribution. A key part of the proof is establishing an asymptotic approximation for the parallel transport of a certain vector field. Whether or not a non-standard term arises in the CLT depends on whether the co-dimension of the cut locus is one or greater than one: in the former case a non-standard term appears but not in the latter case. This is the first paper to give a general and explicit expression for the non-standard term which arises when the co-dimension of the cut locus is one.

Parametric Control via the Algebraic Expression of Lotus-Type Pore Shapes in Metals

Lotus-type porous metals, characterized by low densities, large surface areas, and directional properties, are contemporarily utilized as lightweight, catalytic, and energy-damping materials; heat sinks; etc. In this study, the effects of dimensionless working parameters on the morphology of lotus-type pores in metals during unidirectional solidification were extensively investigated via general algebraic expressions. The independent dimensionless parameters include metallurgical, transport, and geometrical parameters such as Sieverts’ law constant, a partition coefficient, the solidification rate, a mass transfer coefficient, the imposed mole fraction of a solute gas, the total pressure at the top free surface, hydrostatic pressure, a solute transport parameter, inter-pore spacing, and initial contact angle. This model accounts for transient gas pressure in the pore, affected by the solute transfer, gas, capillary, and hydrostatic pressures, and Sieverts’ laws at the bubble cap and top free surface. Solute transport across the cap accounts for solute convection at the cap and the amount of solute rejected by the solidification front into the pore. The shape of lotus-type pores can be described using a proposed fifth-degree polynomial approximation, which captures the major portions between the initial contact angle and the maximum radius at a contact angle of 90 degrees, obtained by conserving the total solute content in the system. The proposed polynomial approximation, along with its working parameters, offers profound insights into the formation and shape of lotus-type pores in metals. It systematically provides deep insights into mechanisms that may not be easily revealed with experimental studies. The prediction of a lotus-type pore shape is thus algebraically achieved in good agreement with the available experimental data and previous analytical results.

Thermal conductivity of nonunitary triplet superconductors: application to UTe2

Considerable evidence shows that the heavy fermion material UTe2 is a spin-triplet superconductor, possibly manifesting time-reversal symmetry breaking, as measured by Kerr effect below the critical temperature, in some samples. Such signals can arise due to a chiral orbital state or possible nonunitary pairing. Although experiments at low temperatures appear to be consistent with point nodes in the spectral gap, the detailed form of the order parameter and even the nodal positions are not yet determined. Thermal conductivity measurements can extend to quite low temperatures, and varying the heat current direction should be able to provide information on the order parameter structure. Here, we derive a general expression for the thermal conductivity of a spin-triplet superconductor and use it to compare the low-temperature behavior of various states proposed for UTe2.

Resilience of the slow component in timescale-separated synchronized oscillators.

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by, first, reducing the dynamics of the fast one using Mori-Zwanzig formalism. Second, we evaluate the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system undergoes a timescale separation. We also find that layered networks seem to be insensitive to such timescale separations.

Application of angiogenesis-related genes associated with immune infiltration in the molecular typing and diagnosis of acute myocardial infarction.

Angiogenesis has been discovered to be a critical factor in developing tumors and ischemic diseases. However, the role of angiogenesis-related genes (ARGs) in acute myocardial infarction (AMI) remains unclear. The GSE66360 dataset was used as the training cohort, and the GSE48060 dataset was used as the external validation cohort. The random forest (RF) algorithm was used to identify the signature genes. Consensus clustering analysis was used to identify robust molecular clusters associated with angiogenesis. The ssGSEA was used to analyze the correlation between ARGs and immune cell infiltration. In addition, we constructed miRNA-gene, transcription factor network, and targeted drug network of signature genes. RT-qPCR was used to verify the expression levels of signature genes. Seven signature ARGs were identified based on the RF algorithm. Receiver operating characteristic curves confirmed the classification accuracy of the risk predictive model based on signature ARGs (area under the curve [AUC] = 0.9596 in the training cohort and AUC = 0.7773 in the external validation cohort). Subsequently, the ARG clusters were identified by consensus clustering. Cluster B had a more generalized high expression of ARGs and was significantly associated with immune infiltration. The miRNA and transcription factor network provided new ideas for finding potential upstream targets and biomarkers. Finally, the results of RT-qPCR were consistent with the bioinformatics analysis, further validating our results. Angiogenesis is closely related to AMI, and characterizing the angiogenic features of patients with AMI can help to risk-stratify patients and provide personalized treatment.