Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge in a Formal Axiomatic Epistemology System Sigma

The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy;2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.

Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

Exploration and Application Practice of Energy Conservation Theory and Method in Steel Manufacturing Process System

This article briefly discusses the theoretical basis and overall goals of energy conservation in the steel manufacturing process system.It is proposed that in the process of implementing system energy conservation,it is necessary to fully recognize and utilize the characteristics and functional advantages of the steel manufacturing process,pay more attention to energy quality,firmly grasp the overall goal of system optimization,focus on the integrated optimization of gas,steam,and waste heat systems,and propose the idea of constructing a"steel chemi-cal gas electricity heating cooling multi generation system".Based on practice,the main principles,models,and effects of implementing systematic energy conservation in steel enterprises have been proposed.

The Magnetic Longitudinal (P-) Wave’s Propagation and Energy Models Underlying the Mechanisms of Its Capacity to Absorb Free Energy

The longitudinal wave term within Faraday’s law of electromagnetic induction (Faraday’s law) underwent recovery to ensure its suitability for theoretical derivation of the equation governing longitudinal electromagnetic (LEM) waves. The revised Maxwell’s equations include the crucial parameters being the attenuation time constants of magnetic vortex potential and electric vortex potential generated by external electromagnetic field within the propagation medium. Specific expressions for them are obtained through theoretical analysis. Subsequently, a model for propagating magnetic P-wave generated by the superposition of a left-handed photo and a right-handed photon in a vacuum is formulated based on reevaluated total current law and revised Faraday’s law, covering wave equations, energy equation, as well as propagation mode involving mutual induction and conversion between scalar magnetic field and vortex electric field. Furthermore, through theoretical derivations centered around magnetic P-wave, evidence was presented regarding its ability to absorb huge free energy through the entangled interaction between zero-point vacuum energy field and the torsion field produced by the vortex electric field.

THE ENERGY CONSERVATION OF VLASOV-POISSON SYSTEMS

We prove that energy conservation holds for weak solutions to classical VlasovPoisson systems with proper regularity.In particular,there exists a solution that conserves energy with|v|^(m)f0∈L^(1)_(x,v)for m>9/4.

THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION

In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space L_(loc)^(3);B_(p,c0)^(α)(R^(3)))for some α∈(1/2,1)and p=9/(3α+1).Moreover,we also use the dimensional homogeneity to explain that the restrictions on the indicators are reasonable.

Assessment of the Implementation of Energy Conservation Opportunities Arising from Energy Audits;A Study of Four-Star and Five-Star Hotels in Nairobi Kenya

This study assesses the implementation of energy conservation opportunities in four-star and five-star hotels in Nairobi. The Covid-19 pandemic had a significant impact on the Hospitality Industry. Currently, there is a growing inclination to furnish guests with superior and sustainable services in an energy-efficient and eco-friendly way. Comprehensive research was conducted from energy audits gathered from the establishments and contracted auditing companies, on top of this, hotel staff were given digital questionnaires. To add to the data, the researcher surveyed the hotels with engineering managers. The Energy Audits found that all 10 hotels had adopted Energy Conservation Opportunities (ECOs). After further analysis, the mean adoption rate of Energy Conservation Opportunities (ECOs) during the past three years was 55.83%, which was below the aim of 100%. According to studies, hotel staff manages energy to cut costs. The researcher found that hotels use up a lot of energy. However, they have conservation potential, depending on government policies, costs, ease of implementation, and management commitment to sustainable practices. Essentially, Energy Conservation Opportunities (ECOs) reduce energy expenditures and boost reliable revenues, especially during high energy prices and uncertainty.

Application Research and Case Analysis of Green Technology in Building Engineering under the Direction of Energy Conservation Demands

With the rapid development of the economy,the scale of construction projects in China is gradually expanding.In terms of construction technology,continuous innovation is being made to meet the needs of sustainable development strategies,and green energy conservation technologies have emerged.It has a brand new design concept,and advocates for maximum energy conservation and environmental protection,fundamentally promoting the rational use of resources and space,and preventing the expansion of air and land pollution.First of all,a brief explanation is given on the current development status of green energy conservation technology in this paper.Secondly,through the introduction and analysis of energy conservation technologies and related building cases,the in-depth research on energy conservation measures of buildings is conducted.Finally,the prospects of green energy conservation technologies are proposed based on the current development status in China.This paper has certain reference value for its related engineering and theoretical research.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

A Mode of Electromagnetic Wave Propagation Based on the Inter-induction of Scalar Electric Field and Vortex Magnetic Field

Drawing upon the electromagnetic conversion formulas in a continuous conductive medium,an extensive examination for total current law and Faraday’s law of electromagnetic induction(Faraday’s law)is undertaken to expound on the laws of electromagnetic induction and conversion.The longitudinal wave term of Faraday’s law is reinstated to render it suitable for theoretical derivation of the LEM(Longitudinal Electromagnetic Wave)equation.Subsequently,we formulate the wave and energy equations for electric P-wave based on reevaluated total current law and modified Faraday’s law;meanwhile proposing a propagation mode that reveals its mechanisms absorbing free energy for LEM waves in a conductor predicated on interaction between scalar electric field and vortex magnetic field.Furthermore,through theoretical derivations based on LEM waves,insights into concealed relationships between electric P-wave and electromagnetism scalar potential are disclosed alongside the constraint equation between the wave velocities of LEM wave and TEM(Transverse Electromagnetic)waves,unveiling the significance of LEM wave.

Energy Saving Analysis of Coal Gas Resource Utilization in Iron and Steel Enterprises

The article discusses the preparation of a gas balance sheet,as well as the recovery,storage,transporta-tion,and use of gas.An analysis was conducted on the occurrence and consumption quotas of various gas media,and specific energy-saving measures were elaborated for each process.This provides a theoretical reference for saving gas and reducing energy consumption in steel enterprises.

Envelope Method and More General New Global Structures of Solutions for Multi-dimensional Conservation Law

For the two-dimensional(2D)scalar conservation law,when the initial data contain two different constant states and the initial discontinuous curve is a general curve,then complex structures of wave interactions will be generated.In this paper,by proposing and investigating the plus envelope,the minus envelope,and the mixed envelope of 2D non-selfsimilar rarefaction wave surfaces,we obtain and the prove the new structures and classifications of interactions between the 2D non-selfsimilar shock wave and the rarefaction wave.For the cases of the plus envelope and the minus envelope,we get and prove the necessary and sufficient criterion to judge these two envelopes and correspondingly get more general new structures of 2D solutions.

Residual symmetry, interaction solutions, and conservation laws of the(2+1)-dimensional dispersive long-wave system

We explore the （2＋l）-dimensional dispersive long-wave （DLW） system. From the standard truncated Painleve expansion, the Baicklund transformation （BT） and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the （2＋l）-dimensional DLW system is consistent Riccati expansion （CRE） solvable. If the special form of （CRE）-consistent tanh-function expansion （CTE） is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.

Conservation laws of the generalized nonlocal nonlinear Schrodinger equation

The derivations of several conservation laws of the generalized nonlocal nonlinear Schrodinger equation are presented. These invaxiants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.

On the energy conservation and critical velocities for the propagation of a "steady-shock" wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅷ)—PRINCIPLE OF TOTAL WORK AND ENERGY

Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.

An extension of the modified Sawada-Kotera equation and conservation laws

Based on the modified Sawad^Kotera equation, we introduce a 3 ~ 3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawad-Kotera equation, by which a Lax pair of the modified Sawada-Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawad-Kotera equation, the Kaup-Kupershmidt equation, and the modified Sawad-Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada-Kotera equation are constructed with the aid of their Lax pairs.

Theoretical verification of the rationality of strain energy storage index as rockburst criterion based on linear energy storage law

The rationality of using strain energy storage index(Wet)for evaluating rockburst proneness was theoretically verified based on linear energy storage(LES)law in this study.The LES law is defined as the linear relationship between the elastic strain energy stored inside the solid material and the input strain energy during loading.It is used to determine the elastic strain energy and dissipated strain energy of rock specimens at various loading/unloading stress levels.The results showed that the Wetvalue obtained from experiments was close to the corresponding theoretical one from the LES law.Furthermore,with an increase in the loading/unloading stress level,the ratio of elastic strain energy to dissipated strain energy converged to the peak-strength strain energy storage index(Wp et).This index is stable and can better reflect the relative magnitudes of the stored energy and the dissipated energy of rocks at the whole pre-peak stage than the strain energy storage index.The peak-strength strain energy storage index can replace the conventional strain energy storage index as a new index for evaluating rockburst proneness.

Water and Energy Conservation of Rainwater Harvesting System in the Loess Plateau of China

Water is the source of all the creatures on the earth and energy is the main factor driving the world. With the increasing population and global change, water and energy conservation have become worldwide focal issues, particularly in the water-stressed and energy-limited regions. Rainwater harvesting, based on the collection and storage of rainfall runoff, has been widely used for domestic use and agricultural production in arid and semiarid regions. It has advantages of simple operation, high adaption, low cost and less energy consumption. This study reviewed rainwater harvesting systems adopted in the Loess Plateau of China and analyzed water use efficiency （WUE） for various rainwater harvesting techniques. Supplemental irrigation using harvested rainwater could increase crop yield by more than 30%, and WUE ranged from 0.7 to 5.7 kg m4 for spring wheat, corn and flax, and 30-40 kg m-3 for vegetables. Moreover, energy consumption for rainwater harvesting based on single family was compared with traditional water supply in the city of the Loess Plateau using the life cycle assessment （LCA） method. Results showed that energy consumption yielded per unit harvested rainwater was 25.96 MJ m-3 yr which was much less than 62.25 MJ m3 yr^-1 for main water supply in Baoji City, Shanxi Province, meaning that rainwater harvesting saved energy by 139.8% as compared to the main water supply system. This study highlights the importance and potential of rainwater harvesting for water and energy conservation in the near future.

NOETHER’S CONSERVATION LAWS OF HOLONOMIC NONCONSERVATIVE DYNAMICAL SYSTEMS IN GENERALIZED MECHANICS

In the present paper, three kinds of forms for Noether’s conservation laws of hol-onomic nonconservative dynamical systems in generalized mechanics are given.