The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

The vibrant landscape of Malaysia serves as a dynamic backdrop for the convergence of artificial intelligence (AI) and social science, reshaping knowledge and inquiry amidst tradition and modernity. With Malaysia leading a technological renaissance driven by digital transformation and innovation, the ethical implications of AI-driven decision-making in public policy and governance emerge as pressing research problems. Addressing concerns such as algorithmic bias and discrimination requires interdisciplinary collaboration to ensure transparency, accountability, and fairness. Exploring questions regarding the distribution of welfare benefits and strategies for enhancing transparency and accountability in urban planning underscores the need for contextually relevant frameworks and stakeholder engagement. Through comprehensive research objectives, including investigating algorithmic biases and analyzing their social implications, scholars aim to contribute to a deeper understanding of the complex interplay between AI technology, social dynamics, and public policy. As Malaysia navigates the challenges and opportunities presented by AI deployment, prioritizing interdisciplinary collaborations, longitudinal studies, and capacity-building efforts will be essential for shaping a future that upholds principles of social justice and collective well-being.

Consideration of physical processes in the reference frame K' moving relative to the CMB, provided that clocks synchronization in this frame ensures the independence of time from spatial coordinates, leads to the conclusion about the existence in the K' of spatial anisotropy which should manifest itself in the dependence of physical effects on the speed vector V of the frame relative to the CМB. Some of these effects in the fields of electrodynamics and optics are considered. In particular, it is shown that weak magnetic fields proportional to the vector V should exist in this frame around motionless electric charges. Experimental verification, according to our assessment, is apparently possible.

Transformation studies have been leaning towards the more practical aspects of change processes and have not yet dealt sufficiently with their personal and political dimensions. They are arguably constrained in doing so if they are either overly focussed on systems and how to control them or on individualistic values and behaviours. In this study we show how the actually-occurring societal transformations that people face can be usefully approached through the lenses of dialogical sense-making and critical phenomenology. While distinct, these approaches share a concern with aspects missed when transformation is abstracted and alienated from people’s lives; namely people’s lived experiences during times of change, and the conditions of possibility for these experiences. Dialogical sense-making explores how people create meaning around transformations, through interactions with other people, with different lines of arguments, and as part of broader public discourse. Critical phenomenology engages with subjectivity and lived experience, and with the role of foundational as well as socio-culturally dominant yet contingent structures in shaping our ways of perceiving, experiencing and knowing the world. Through a discussion of insights from these approaches, we show how they offer tools that enable new questions about transformative change as it is experienced and made sense of. Situating analyses of tranformation from within a focus on experience brings us closer to understanding the significance of change processes in people’s lives, and allows for an inquiry into the conditions of experience, including transformative experiences.

Salt marshes are globally important ecosystems, but many have been lost or transformed due to the impacts of global change. There have been attempts to broadly quantify salt marsh communities, especially the ubiquitous grasses which serve as foundation species such as Spartina alterniflora and Spartina patens, the latter of which is being lost due to sea level rise. However, few researchers have used high-resolution geospatial imagery to quantify fine-scale changes in the distribution of grasses or to track losses of S. patens. To address this issue, we utilized a simple and rapid method of classifying geospatial marsh imagery with cloud-based machine learning in Google Earth Engine (>92% accuracy for S. patens regardless of imagery age). Our methods allowed us to characterize full landscapes (two geospatially proximal areas, >7,000 ha each) of critical salt marshes on the New Jersey coast and to evaluate fine-scale (1-m) community transformations in response to global change with imagery from 2006 to 2019. Notably, one marsh experienced very little change while the other experienced an 81.17% (1,087 ha) loss of S. patens, illuminating disparate patterns of change for two geographically proximal ecosystems. Further exploration revealed an association in the loss of S. patens with increases in streamflow and total nitrogen content in the rivers that run through each marsh. These results signify the importance of broad-scale ecological studies that evaluate fine-scale community transformations and for management strategies that do not generalize across landscapes of an ecosystem-type.

This article analyzes the perspectives of professional training of the public administration staff, from the viewpoint of the sustainability criteria, starting from the experiences of the online courses run in the last two years. In order to understand the nature, type and magnitude of the changes caused by the Covid-19 pandemic in the field of professional training for public administration, we performed a survey among public institution employees, by applying a questionnaire. The instrument included qualitative elements, to allow the framing of statistical results. The article is grounded on the hypothesis that the professional training activities in the last two years were organized preponderantly online and it aims to analyze the sustainability of the new teaching systems/methods. The limitations of the study are given by the fact that each administrative system has structure particularities and its own legal framework regarding the professional training of public administration staff, what makes that the model proposed cannot be applied in all countries. The study provides a model of online professional training for public administration staff, sustainable, based on the experience accumulated in the last two years.

A fundamentally new synthetic approach to the synthesis of 2-aminopurine has been developed. It consists in the combination of creation of condensed polyazotic heterocyclic tetrazolopyrimidine structure, it’s transformation into triaminopyrimidine and subsequent cyclization into 2-aminopurine. The structure of the obtained compounds was established based on spectral characteristics and intermediate 5 directly by X-ray diffraction analysis.

Recently, a new theory based on superluminal tunnelling has been proposed to explain the transition of highly energetic neutrinos propagating in matter to tachyonic states. In this work, we determine the possible mechanisms that lead neutrinos into a superluminal realm based on the assumption that ultrarelativistic particles travelling in matter lose part of their energy with the emission of Bremsstrahlung radiation. The obtained photons, in turn, can create neutrino-antineutrino pairs, one or both of which can be superluminal. We also prove that pair creation may occur with neutrino flavour oscillation provided that only one of them is a space-like particle. This suggests that mass oscillation and superluminal behaviour could be related phenomena. Finally, using the generalised Lorentz transformations, we formulate the Lagrangian of the kinematically allowed scattering processes. The structure of this Lagrangian is consistent with the formalism of the Standard Model. Based on this Lagrangian, at least one of the particles forming the pair must always be subluminal. The possibility that the pair creation process is mediated by a dark photon is also discussed.

This paper focuses on the paradigm that explains the link between energy transitions and financial transformations. In particular, it attempts to shed some light on the following question: How did the transition from wood to coal affect financial development in late 18^th and early 19^th century Britain? The results demonstrate that the energy transition in Britain during the 1^st Industrial Revolution constituted an important moment in the country's financial development and can be used as an example of how an energy innovation can foster the financial development of particular countries or regions.

Alloys based on TiNi are widely used in various fields of technology and medicine. In the present work, we report on preparation of TiNi-alloy based wire with the shape memory effect, which was used for compression clips for surgery. Composition and structure of the wire, and its martensitic and physical-chemical properties were studied using SEM, TEM, optic microscopy, profilometry, mechanical tests, etc. The TiNi alloy was found to consist of B2 and B19' and secondary-phase particles of Ti2Ni, TiNi3 and Ti3Ni4. Its matrix was slightly enriched in Ni (50.3 at. % of Ni). Homogeneous grain structure was revealed (an average grain size of 19±0.3 μm) with equal quantities of grain boundaries of special and general types. Surface oxide layer provide improved biocompatibility and promote adhesion of protein molecules. Overall, the obtained TiNi wire was concluded to exhibit martensitic, physical and mechanical properties suitable for its use as an implant material. The wire was then used for manufacturing compression clips with the shape memory effect and applied in surgery. The medical experiment that involved 46 children demonstrated that the use of such clips in children with double-barreled enterostomies permitted to improve the results of surgical treatment.

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.

In this paper, the quantum theory of the infinite-component Majorana field for the fermionic tower is formulated. This study proves that the energy states with increasing spin are simply composite systems made by a bradyon and antitachyons with half-integer spin. The quantum field describing these exotic states is obtained by the infinite sum of four-spinor operators, which each operator depends on the spin and the rest mass of the bradyon in its fundamental state. The interaction between bradyon-tachyon, tachyon-tachyon and tachyon-luxon has also been considered and included in the total Lagrangian. The obtained theory is consistent with the CPT invariance and the spin-statistics theorem and could explain the existence of new forms of matter not predictable within the standard model.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

The commonly used words ‘transformation’ and ‘transition’ tend to lose their edge when used for any significant change process as is rather often the case. Partners and wider stakeholders in initiatives related to ‘sustainability transitions’ therefore often entertain different perspectives on what the strategic orientation of an initiative is or is meant to be. Common planning and design processes such as situation analysis and theories of change, however, often do not sufficiently cater to this dynamic. As a result, different actors may be pulling the initiative in different directions, undermining the overall partnership efforts. In this short contribution a strategic scoping canvas and an associated facilitation process are presented as a way of addressing such situations. Illustrations are provided of initial application in three cases related to food system transitions in Peru, Ethiopia, and Bangladesh, exploring the connectivity with approaches commonly used in the context of system transformations, including the Multi-Level Perspective on sustainability transitions, the Leverage Points approach, Capability Approach, and the theory of Large System Change. We conclude that the canvas and associated facilitation approach has proved useful in different contexts, offering opportunities for complementing existing methodologies, and potentially enhancing their efficacy in facilitated multi-stakeholder processes.

Bioconvective flows have attracted attention in recent years due to actual and potential applications. In this paper, we consider a steady and laminar convective MHD flow of a nanofluid with heat, mass and microorganism transfer with a heat source/sink present. In addition, we assume there exists a first order chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) using the scaling group transformation and the associated boundary value problem is then solved. The influences of selected governing parameters on the dimensionless velocity, temperature, nanoparticle concentration, density of motile microorganisms, skin friction, heat transfer, mass transfer, and motile microorganism density rates are computed and discussed

When discussing the gauge symmetries of any theory, the Henneaux-Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux-Teitelboim transformations and the resulting gauge group in the general case, and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

Given any sequence a = (an)n1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n1 such that y=a = (yn=an)n1 2 E. In this paper, we use the spaces w1, w0 and w of strongly bounded, summable to zero and summable sequences, that are the sets of all sequences y such that ? n?1Pn k=1 jykj
n is bounded, tends to zero and such that y ? le 2 w0, for some scalar l, respectively, (cf. [24, 22]). These sets where used in the statistical convergence, (cf. [17, Chapter 4]). Then we deal with the solvability of each of the (SSIE) F
 E + F0x where E is a linear space of sequences, F = c0, c, `1, w0, w, or w1 and F0 = c0, c, or `1. For instance, the solvability of the (SSIE) w
 w0+s(c) x consists in determining the set of all sequences x = (xn)n1 2 U+ that satisfy the following statement. For every sequence y that satisfy the condition limn!1 n?1Pn k=1 jyk ? yk?1 ? lj = 0, there are two sequences u and v, with y = u+v such that limn!1 n?1Pn k=1 jukj = 0 and limn!1 (vn=xn) = L for some scalars l and L. These results extend those stated in [11, 12, 10].

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.

Albert Einstein, shortly after publishing his General Relativity Theory (GRT) applied it to the entire universe in a paper of 1917. Einstein assumed that such a universe was static in time and possessed a uniform distribution of matter on the largest scales, obtaining a static and finite universe of spherical spatial curvature of radius R. Although this model was refuted by Edwin Hubble's discovery of the expansion of the universe, it is still often studied as a theoretical framework for some problems, such as the twin paradox. This paper will show that Einstein's static universe model leads to a privileged frame of reference, so that any observer moving at the speed v will be able to measure speeds of light other than c depending on the direction of beam transmission. The above will refute the validity of the application to this closed and static universe of the Special Relativity Theory (SRT) proposed by Einstein in 1905 in his article . In addition, a new synchronization convention and new coordinate transformations will be deduced, the "generic" transformations, which will replace those of Lorentz. Finally, the twin paradox in this universe will be solved by making use of them.

A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

Background: Recurrent approximation of retention parameters in reversed-phase HPLC is effective for revealing anomalies difficult to detect otherwise, namely, the reversible hydration of analytes. This was demonstrated previously for restricted sets of analytes with acetonitrile–water eluents. Expanding the number of analytes and eluents seems to be a topical problem. Two kinds of derivatives of aromatic carbonyl compounds were characterized: unsubstituted hydrazones and oximes. Methods: If analyte demonstrates no anomalies in dependences of retention times vs. concentration of organic modifier, the recurrent approximations of these dependences are linear. To explain the features of recurrent approximations, the numerical experiments were proposed and considered. The artificial shifting of one, two, or more points allows modeling the different kinds of deviations of approximations from linearity. Results: It was shown that hydrazones are the class of analytes having no anomalies of retention parameters. On the contrary, several anomalies were detected for oximes. Downward deviations of points in the plots of recurrent approximations of retention times are the signs of reversible hydration. This effect for methanol–water eluents was detected for the first time. Some of oximes underwent hydrolysis. Conclusion: Recurrent approximation of retention times allows detecting chemical transformations of analytes during RP HPLC analysis.

Goal of this article is to provide the numerical and experimental assessments of an effective near-field to far-field transformation (NF–FF T) technique with planar spiral scanning for flat antennas under test (AUTs), which requires a non-redundant, i.e. minimum, amount of NF measurements. This technique has its roots in the theory of non-redundant sampling representations of electromagnetic fields and has been devised by suitably applying the unified theory of spiral scans for non-volumetric antennas to the case in which the considered AUT is modeled by a circular disk having its radius equal to one half the AUT maximum dimension. It makes use of a 2-D optimal sampling interpolation (OSI) formula to accurately determine the massive NF data required by the classical plane-rectangular NF–FF T technique from the non-redundant ones gathered along the spiral. It must be emphasized that, when considering flat AUTs, the developed transformation allows to further and significantly save measurement time as compared to that needed by the previously developed NF–FF T techniques with planar spiral scans based on the quasi-planar antennas modelings, because the number of turns of the spiral and that of NF data to be acquired depend somehow on the area of the modeling surface. The reported numerical simulations assess the accuracy of the proposed NF–FF T technique, whereas the experimental tests prove its practical feasibility.

The interpretation of optical spectra requires thorough comprehension of quantum mechanics, especially understanding the concept of angular momentum operators. Suppose now that a transformation from laboratory-fixed to molecule-attached coordinates, by invoking the correspondence principle, induces reversed angular momentum operator identities. However, the foundations of quantum mechanics and the mathematical implementation of specific symmetries assert that reversal of motion or time reversal includes complex conjugation as part of anti-unitary operation. Quantum theory contraindicates sign changes of the fundamental angular momentum algebra. Reversed angular momentum sign changes are of heuristic nature and are actually not needed in analysis of diatomic spectra. This work addresses sustenance of usual angular momentum theory, including presentation of straightforward proofs leading to falsification of the occurrence of reversed angular momentum identities. This review also summarises aspects of a consistent implementation of quantum mechanics for spectroscopy with selected diatomic molecules of interest in astrophysics and in engineering applications.

When developing bone implants Young's modulus is one of the primary characteristics of the material that should be considered. The study focuses on the possibility of regulating the modulus of the alloy Ti-50.8 at % Ni by varying its initial structure as well as aging-induced microstructure in a wide range. Microstructure observations were performed using TEM and SEM observations. The calorimetric studies of martensitic transformations were carried out using "Mettler Toledo 822e". Tensile tests were performed in a test temperature range of ‒196≤T≤+100°C using an «IN-STRON 5966». The grain/subgrain size of B2-austenite strongly affects the modulus magnitude. This effect is ambiguous for a material with a grain size of 0.13–3 µm and depends on the test temperature. The effectiveness of aging on the modulus reduction depends on the initial structure: it is most pronounced in an alloy with a relatively coarse grain size of 9 µm and brings a decrease by 3.8 times at a temperature of 37°C. Bone-like elastic modulus (10–30 GPa) at a human body temperature of 37°C is realized in an aged fine-grained NiTi alloy. An ultrafine-grained sub-structure exhibits he same values of Young's modulus in the temperature range from -100°С to 25°С.

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra sl(2,R) and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R42: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R⁴₂: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

We explores the hydrodynamical limit of a homogeneous electron gas, considering the interplay between the infrared limit and phenomenological hydrodynamics. Our study involves interactions generated by non-linear coordinate transformations. The focus begins with an analysis of non-linear coordinate transformations and their impact on normal modes in a harmonic system. The Lagrangian for a harmonic oscillator is used as an illustrative example, highlighting the role of position-dependent effective mass in preventing certain coordinate values. Moving beyond single degrees of freedom, we extend the discussion to a system with several harmonic degrees of freedom, introducing a collective variable. The effective dynamics of this collective variable are defined through a Lagrange multiplier term, emphasizing linearity in the description. Our study extends to the Current Two-Point function (CTP) formalism, introducing matrices and their inverses, such as $\hD$ and $\hD^{-1}$. Further, we delve into the dynamics of current in a homogeneous electron gas at finite density and zero temperature. Green's functions are generated using a functional integral approach, and the effective action is constructed via functional Legendre transformation. The quadratic part of the generator functional is expanded to derive the effective action, leading to the Maxwell equation and the subsequent elimination of the photon field. The resulting effective action for current dynamics is expressed in terms of the Current Two-Point function, paving the way for further exploration of the hydrodynamical aspects of the electron gas. Our study combines theoretical developments and mathematical formalism to provide insights into the hydrodynamical behavior of homogeneous electron gases.

Herein, we report on a versatile system composed of two Ni(II)-based coordination compounds: a 3D metal-organic framework of {[Ni(μ-3isoani)2]·DMF}n (1) formula and a 0D monomeric [Ni(3isoani)2(H2O)4] (2) complex (where 3isoani = 3-aminoisonicotinato and DMF = dimethylformamide) which show mutual solvent-induced reversible transformations into each other. These 1 ↔ 2 transformations are triggered by the exposure of one compound to the solvent present in the other, that is, the MOF (1) in water and the monomer (2) in DMF. The process is easily followed by the naked eye because it involves a colour change from green (1)-to-brownish green (2), making the system potentially interesting to act as a sensor of those solvents. Moreover, these compounds present very different magnetic properties since 1 shows field-induced single-molecule magnet (SMM) behaviour, which corresponds to one of the few Ni(II)-based compounds showing this property, whereas 2 behaves as a regular paramagnet, all of which is explained according to a careful study of the magnetic properties by means of experimental direct-current (dc) and alternating-current (ac) measurements as well as complete active space self-consistent field (CASSCF) calculations.

The time symmetry of T_c = CT is redefined based on the 4-D Euclidean space. The time inversion symmetry of T_c = CT changes the signs of the charge (q) and absolute time (ct) of the particle. The P symmetry changes the signs of the space momenta and handedness of the particle. The T_c symmetry changes the signs of the time momentum (P_t=E/c) and charges. The handedness are classified as the left-handedness and right-handedness on the 3-D space. The charges (|q| = cDt) and energies (E= cDtDV) of the particles are originated from the upward warping (q>0) and downward warping (q<0) of the particles along the time axis. The evolution of our matter universe with P_t > 0 since the big bang can be interpreted based on the CTP symmetry with the partner antimatter universe with p_t < 0. The photon space is called as the vacuum space. Then the E and M waves are the space fluctuations, and the gravitational G wave is the time fluctuations. And the E, M and G fields are newly explained. The zero E and M fields of the photon space indicates that the photon space and gamma ray are the 2EM waves. The rest mass energy of the particle is the 4-D space volume of the warped photon space. In the present work, the quantum wave function is considered as the 4-D vector with the space wave function and time axis wave function in the 4-D Euclidean space. The warped photon space corresponds to the squared wave function which is the probability density. It is concluded that, in the quantum mechanics, the imaginary number concept is introduced in the quantum wave functions instead of the time axis component of the 4-D wave function vector. The left-handed neutrino puzzle is explained from the handedness partner relation with the right-handed dark matters. Finally, the modified Lorentz transformations derived in the 4-D Euclidean space are compared with the Lorentz transformations of the special and general relativity theories in the 4-D Minkowski space.

This article is some review of results that were obtained at 2007-2021 years development of “The Information as Absolute” concept and the informational physical model, which is based on the concept; including a number of fundamental physical problems are briefly considered in framework of the conception and the model. Recently in physics there are several publications, that present lists of the problems. However, those lists are essentially incomplete, for at least two reasons. Firsts of all, a number of phenomena are studied traditionally by philosophy, and so corresponding problems are usually considered to be “metaphysical”. However, they relate also to some concrete physical phenomena. For example, physics evidently studies Matter, and so the metaphysical problems “what is ontology of Matter”, “what is “Space”, “Time” and a few other physical phenomena and notions as well, are really a Meta-physical problems “what does physics study?” There are other fundamental physical problems, which are not considered as such in physics, and are absent in the “fundamental problems lists”. Those include the problems, which really exist, yet are incorporated into standard physical theories, and so are fundamental “implicitly”, which in physics are “solved by default” ‒ and mostly erroneously. Note, though, that a number of “Meta-physical”, and concrete fundamental, problems more in detail are considered in the paper “The Informational Conception and Basic Physics”, https://arxiv.org/abs/0707.4657, v5 (2021), so this paper is, in certain sense, an expanded conclusion of this paper, which includes, correspondingly, more in detail consideration of some more general physical problems; and, besides, in this article, the problem “what are Gravity and Electric Forces” is essentially clarified comparing with the arXiv 2021 paper version above. Besides, the concrete problem “What is Life”, and the rational cosmological model, where a few vague points in standard cosmology rather probably are rationally clarified, while the fundamental problem “matter – antimatter asymmetry” in Matter is solved practically for sure, are considered, and one of recently published rather complete “lists of fundamental problems” is commented in Appendix.