Admissible Conditions Research Articles

Quantitative Coding and Complexity Theory of Continuous Data: Part I: Motivation, Definition, Consequences

When encoding real numbers as (necessarily infinite) bit-strings, the naïve binary/decimal expansion is well-known [ doi:10.1112/plms/s2-43.6.544 ] computably “ un reasonable”, rendering, for example, tripling qualitatively discontinuous on Cantor’s sequence space. Encoding reals as sequences of (finite integer numerators and denominators, in binary, of) rational approximations does make common operations qualitatively computable, yet admits no bounds on their computational complexity/quantitative continuity. Dyadic approximations, on the other hand, are known polynomially, and signed binary expansions even linearly, “reasonable” in a rigorous sense recalled in the introduction of this work. But how to distinguish between un/suitable encodings of spaces common in Calculus beyond the reals, such as Banach or Sobolev? With respect to qualitative computability/continuity on topological spaces, the technical condition of admissibility had been identified [ doi:10.1016/0304-3975(85)90208-7 ] for an encoding over Cantor space (historically called a representation ) to be “reasonable” [ doi:10.1007/978-3-030-59234-9_9 ] . Roughly speaking, admissibility requires the representation to be (i) continuous, and to be (ii) maximal with respect to continuous reduction. Admissible representations exist for a large class of spaces. And for (precisely) these does the Kreitz–Weihrauch—sometimes aka Main —Theorem of Computable Analysis hold, which characterizes continuity of functions by continuity of mappings translating codes, so-called realizers . We refine qualitative computability/continuity on topological spaces to quantitative continuity/complexity on metric spaces by proposing a notion, and investigating the properties, of polynomially/linearly admissible representations. Roughly speaking, these are (i) close to “optimally” continuous, namely linearly/polynomially relative to the space’s entropy, and they are (ii) maximal with respect to relative linear/polynomial quantitatively continuous reductions defined in the main text. Quantitatively admissible representations are closed under composition over generalized ground spaces beyond Cantor’s. Such representations exhibit a quantitative strengthening of the qualitative Main Theorem , namely now characterizing quantitative continuity of functions by quantitative continuity of realizers. A large class of compact metric spaces is shown to admit polynomially admissible representations over compact ultra metric spaces, and some even a generalization of the linearly admissible signed binary encoding. Quantitative admissibility thus provides the desired criterion for complexity-theoretically “reasonable” encodings.

"For their own good". Medical assistance in dying: a right for whom?

The admission criteria to the medical assistance in dying (MAID) procedures (Euthanasia - E; Physician Assisted Suicide - PAS) represent a much debated issue. In most of the jurisdictions where MAID is legal, the unbearable suffering due to a terminal illness constitues the main admission condition. In contrast, those suffering from either a mental disorder or an existential discomfort are excluded. Some consider the exclusion of the former group to be protective towards those deemed vulnerable because they are not able to make free and informed decisions, while the latter is excluded to align the legal approaches to the prevailing moral models. Others consider these stances discrimination. To prove that when someone requests MAID, his suffering should be first and foremost investigated not only and not so much for its causes, but, above all, for its key role played in understanding the MAID request. After reviewing the specific aspects of suffering in relation to his three determinants - existential suffering, mental disorder, terminal illness - the article provides the evidence that: a) such a conditions, although completely different from each other, share the same psychological processes leading to the unbeaerable suffering and then to the request for MAID or to the suicide ideation/completion; b) there is no scientific data supporting a discrimination access to MAID on the basis of the presence/absence of a terminal illness. Using the unbearable suffering due to a terminal illness as the sole criterion for admission to MAID violates the principle of autonomy, and, lacking scientific evidence, it does not clarify where the line is drawn between those who should be entitled to MAID and those who should not.

Modeling of shear wave propagation in piezo-viscoelastic microbeam over quadratic heterogeneous viscoelastic plate with sliding contact

Abstract This study analyzes the phase and attenuation dynamic behavior of piezo-viscoelastic microbeam overlying quadratic heterogeneous viscoelastic plate under sliding contact. Using the Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Maxwell’s relations are used to incorporate the electric potential function. The solutions for both media are derived separately by solving the second-order hyperbolic differential equation using the method of separation of variables and asymptotic expansions of Bessel functions. The system of linear homogeneous equations is obtained by applying admissible boundary conditions to determine fundamental physical quantities. The key contribution of the current work is demonstrating the influence of dissipation factors, sliding contact, micro-length, heterogeneity, and thickness ratio parameters on shear wave propagation. The micro-length effect is found to suppress the attenuation of shear waves through the analysis and discussion of the dispersion and attenuation curves.

Some Remarks on Wang-Yau Quasi-Local Mass

Abstract We review the definition of Wang-Yau quasi-local mass from the point
of view of the gravitational Hamiltonian. This makes clear the relation between
Wang-Yau definition and Brown-York or even global ADM definition. We make a
brief comment on admissibility condition in the definition of the Wang-Yau quasi-lcoal
mass. We extend the positivity proof forWang-Yau quasi-local energy to allow possible
presence of strictly stable apparent horizons through establishing solvability of Dirac
equation in certain 3-manifolds that possess cylindrical ends, as in the case of Jang’s
graph blowing up at marginally outer trapped surfaces.

The genesis of the establishment and development of the legal profession in the Ukrainian territories during the Lithuanian and Austrian Rule

The article is devoted to the study of the formation and development of the legal profession in the Ukrainian territories during the period of Lithuanian and Austrian rule. It is established that when Ukrainian lands became part of the Grand Duchy of Lithuania, the legal norms in force on its territory not only streamlined the judicial process, but also gave the prosecutor’s activity a labor character, transforming it into a profession. With the development of municipal self-government, in particular Magdeburg law, prosecutorial activity began to acquire a formalized framework, and with the introduction of the Lithuanian statutes, the legal status of prosecutors was enshrined in the highest legal acts. Despite certain shortcomings, the institution of judicial intercession was firmly rooted in the judicial process and became an integral element of the democratization of the judicial system in the Ukrainian territories in the fourteenth and sixteenth centuries. During the period when the Ukrainian territories were under the rule of the Austrian monarchs, the legal profession was regulated in accordance with Austrian law, providing a clear regulatory framework for the functioning of the Bar. Austrian legal acts defined the conditions for admission to the bar, the duties of attorneys and their liability, contributing to the formation of high standards for the personality of an attorney. The rigorous selection of applicants not only ensured that attorneys provided quality services, but also contributed to strengthening the authority of the bar in society, increasing confidence in it as an institution that performs a special social function, defending the rights and interests of citizens. As a result, the Bar of that time gradually gained public recognition, becoming an important factor in the legal life of the country and a significant social force. It is established that during the nineteenth century, the role of an attorney-at-law went beyond the traditional advocacy in court: attorneys-at-law provided legal advice, facilitated the settlement of legal transactions, and explained to citizens their rights and opportunities in the context of current legislation. In this way, lawyers contributed to the dissemination of legal knowledge and the formation of legal awareness in society. During the Austrian rule, the practice of law became the foundation for the observance of the rights and freedoms of Ukrainians, subjects of the Empire, and strengthened the level of public trust in legal institutions in the Ukrainian territories.

Measure‐valued processes for energy markets

AbstractWe introduce a framework that allows to employ (non‐negative) measure‐valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how the Heath–Jarrow–Morton approach can be translated to this framework, thus guaranteeing arbitrage free modeling in infinite dimensions, while allowing for the incorporation of important stylized facts, in particular stochastic discontinuities, that is, jumps or spikes at pre‐specified (deterministic) dates. We derive an analog to the HJM‐drift condition and then treat in a Markovian setting existence of non‐negative measure‐valued diffusions that satisfy this condition. To analyze mathematically convenient classes we consider measure‐valued polynomial and affine diffusions, where we can precisely specify the diffusion part in terms of continuous functions satisfying certain admissibility conditions. For calibration purposes these functions can then be parameterized by neural networks yielding measure‐valued analogs of neural SPDEs. By combining Fourier approaches or the moment formula with stochastic gradient descent methods, this then allows for tractable calibration procedures which we also test by way of example on market data.

Directions for improving the migration policy of the European Union in matters of migrant integration

The article is devoted to the analysis of current directions of improvement of the European Union’s migration policy in the context of immigrant integration, in particular, in the context of growing migration flows to Europe. Authors note that there are problems in building migration policy due to the fragmentation of its regulatory mechanisms. The emphasis is placed on the need for a systematic approach to solving problems related to the integration of immigrants that affect the social stability and economic balance of the EU Member States. The main challenges faced by both immigrants and host countries are considered: cultural isolation, formation of parallel communities, economic vulnerability of migrants, discrimination, illegal migration and social conflicts. The provisions of the Pact on Migration and Asylum, as well as the Action Plan on Integration and Inclusion for 2021–2027, which develops the provisions of the Pact, are analyzed. Special attention is paid to measures and recommendations aimed at promoting the integration of migrants and strengthening social cohesion in the EU countries. Authors examine the provisions of the Pact that provide for “solidarity cooperation” between Member States, including mechanisms for the redistribution of migrants, financial compensation and technical assistance for first-receiving states, in particular through the standardization of admission conditions. Further areas for improving integration policy are suggested, such as improving mechanisms for recognizing professional qualifications, increasing access to educational and language programs, combating discrimination, and strengthening the decentralization of integration measures. According to the authors, despite the fact that the EU does not have the competence to legislate in this area, the Action Plan can be a decisive push on the way to the effective integration of immigrants, where social cohesion, economic stability and security in the EU will be key elements, and further reforms in this area will help overcome the current challenges of the migration crisis.

Mapping Properties of Associate Laguerre Polynomial in Symmetric Domains

The significant characteristics of Associate Laguerre polynomials (ALPs) have noteworthy applications in the fields of complex analysis and mathematical physics. The present article mainly focuses on the inclusion relationships of ALPs and various analytic domains. Starting with the investigation of admissibility conditions of the analytic functions belonging to these domains, we obtained the conditions on the parameters of ALPs under which an ALP maps an open unit disc inside such analytical domains. The graphical demonstration enhances the outcomes and also proves the validity of our obtained results.

An Anti‐Attack Neural Sliding Mode Framework Based on a Novel Non‐Fragile Observer

ABSTRACTThis article investigates anti‐attack stabilization with passivity problem of uncertain singular semi‐Markov jump systems (singular S‐MJSs) with exogenous disturbance and delay. An ingenious non‐fragile observer‐based neural sliding mode control (SMC) scheme is put forward to solve the problem. First, considering unmeasured states, a distinctive non‐fragile and decoupled observer, which does not contain the control input or any auxiliary sliding mode compensator design as in existing observer‐based SMC approaches, is established such that the disadvantages of sliding mode switching in observers in existing literature can be avoided. Then, “only one sliding surface” design and a new system analysis route are presented, and the derived sliding surface is accessibly designed. Next, a new version of stochastic admissibility and passivity sufficient condition is given, and a related algorithm via an optimization problem is proposed to determine the controller gain and the observer gain by linear matrix inequalities (LMIs). Further, a novel observer‐based anti‐attack neural SMC law, which utilizes a neural network‐based approach to approximate actuator attack, is proposed to stabilize the singular S‐MJSs against actuator attack. Finally, simulation and comparison results are presented, which demonstrate the effectiveness and superiority of our method.

H∞ adaptive ETF control for degenerate jump systems under actuator faults and impulsive deception attacks with application to DCMIP device

This article considers the issue of H∞ adaptive event-triggered feedback control for degenerate jump systems under actuator faults and impulsive deception attacks. Based on periodic sampling strategy, a mode-dependent adaptive event-triggered scheme is developed, which can save communication resources, avoid the Zeno phenomenon and take full advantage of Markovian mode information. By constructing the neoteric Lyapunov-Krasovskii (L-K) functional containing piecewise linear impulsive auxiliary functions and applying singular value decomposition (SVD) technique, the fresh stochastic admissibility conditions for degenerate Markovian jump systems under actuator faults and impulsive deception attacks are obtained under the framework of linear matrix inequalities (LMIs), and then the adaptive event-triggered scheme with weighted matrices and feedback controller are designed simultaneously. By applying freedom weight matrix method and the property that the network-induced delay derivative is one, the non-strict LMI conditions are transformed into strict ones, such that the stochastic admissibility of the degenerate jump systems and state feedback controller gains are realized adequately. Finally, a direct current motor-controlled inverted pendulum (DCMIP) device is used to confirm the feasibility of the presented approach.

Кадрове забезпечення медичної допомоги дітям в Україні в умовах війни та пандемії COVID-19

Most countries around the world report risks to children's health care due to a growing shortage of paediatricians. Аim - to analyse the staffing of paediatric health care in Ukraine in the context of the ongoing war and the COVID-19 pandemic. Materials and methods. The methods used were a systematic approach and comparative analysis of data from the state institution "Centre for Public Health of the Ministry of Health of Ukraine" for 2020-2023. Results. During the years of the pandemic and full-scale aggression of the Russian Federation, the number of paediatricians in Ukraine decreased by 1006 people, which led to a corresponding decrease in the paediatric care coverage rate by 12.5% to 1.19 per 1000 children, which may affect the quality and accessibility of medical care for children, especially newborns. The largest staff losses during the pandemic and war have been in paediatric pathology, pulmonology, phthisiology, infectious diseases, immunology, dentistry, dermatology, neurology, gynaecology, gastroenterology and neonatology, which has already led to problems in the availability of specialised paediatric care for children and newborns, especially in the frontline and de-occupied areas. In such difficult conditions, pediatric doctors and the system of providing medical care to Ukrainian children in general have proven their viability and are still able to withstand the double pressure of war and the COVID-19 pandemic, preventing a significant increase in child morbidity and infant mortality. Conclusions. In order to eliminate the shortage of personnel, it is urgent to increase the number of doctors trained at higher medical educational institutions in specialty 228 «Paediatrics» to 1,000 per year, to adjust the state order and admission conditions accordingly, and to introduce paediatric residencies in the most popular specialties. No conflict of interests was declared by the authors.

Reproducing formulas for L2-multiplier operators related to the k-Hankel transform

ABSTRACT The aims of this paper are to study the L 2 -multiplier operators, T m , σ , associated with k-Hankel transform. We derive three Calderón's reproducing formulas. Initially, by an admissibility condition we get the inversion formula for T m , σ ( φ ) . Furthermore, we achieve quadratic convergence as our second formula. Additionally, by utilizing the extremal function, we obtain the best approximation formula.

Legal regulation of education in Ukraine. Part 3: equal rights, security and dignity of students and language requirements for admission to an educational institution under the conditions of military emergency

The purpose of this article is to continue the analysis of Ukrainian legislation and international acts that regulate or affect the process of regulating basic human rights and freedoms in Ukraine’s education field. The conduct of this study is due to the activities of the Cabinet of Ministers of Ukraine and the Ministry of Education and Science of Ukraine in 2024, which intervened directly during the admission process of students to higher educational institutions during the 2024 admission campaign. The mentioned aspects especially affected the education seekers who declared their desire to study full-time and on a paid basis in graduate school to obtain the third (educational and scientific) level of higher education. Regarding the above, it became necessary to legally examine the observance of basic human rights and freedoms when conducting the admission process under martial law along with implementing and regulating educational activities. In particular, the article examines the main conditions and guarantees of equality of rights of education seekers when enrolling in educational institutions. Additionally, the study underlines the main legal provisions on the human right to safety and dignity, which shall be observed during the admission campaign and when carrying out educational activities in conditions of military emergency as well as in conditions of economic crisis. At the same time, special attention is focused on the need to establish different admission conditions and study conditions for free education and paid education recipients. In addition, the authors analyze the legislation of Ukraine regarding the possibility of using the factor of knowledge of foreign languages as a condition for admission to institutions of higher education, both in the general context and taking into account the specifics of the education received by the student. Thus, this article is the third article from the cycle of research and contains the results of a legal study of the principle of equal rights in the field of education, the principle of safety and human dignity in education, in particular, during the period of military emergency in Ukraine, as well as the principle of Ukrainian-language education in Ukraine.

Tensor renormalization group study of (1 + 1)-dimensional U(1) gauge-Higgs model at θ = π with Lüscher’s admissibility condition

We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a θ term, where the U(1) gauge action is constructed with Lüscher’s admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find the first-order phase transition with sufficiently large Higgs mass at θ = π, where the ℤ2 charge conjugation symmetry is spontaneously broken. On the other hand, the symmetry is restored with a sufficiently small mass. We determine the critical endpoint as a function of the Higgs mass parameter and show the critical behavior is in the two-dimensional Ising universality class.

The use of a clinical calculator to determine the rate of development of chronic kidney disease in elderly patients with type 2 diabetes mellitus

Aim – to develop an applied prognostic calculator for the rate of progression of CKD in elderly patients with type 2 diabetes, which makes it possible to identify a group of high rate of GFR reduction in conditions of routine outpatient admission. Material and methods. 69 clinical indicators were studied, the interrelationships and significance of differences in parameters in the groups identified according to the original diagnostic parameter, the glomerular filtration rate reduction index with a threshold value of 3.83 ml/min/1.73 m2 per year, above which the rate of progression of CKD was considered high. Results. By using regression analysis, significant factors for the prognostic calculator were identified: the duration of diabetes and insulin therapy, concomitant diagnosis of obesity, pulse in the ankle artery, severe stage of polyneuropathy, risk group IV of hypertension, treatment with sulfonylureas, the number of antihypertensive drugs taken. When evaluating the information capacity and predictive ability of the calculator, the area under the AUC ROC curve was 0.89 (0.80; 0.99) p 0.001, which characterizes the quality of the diagnostic technique as high. Conclusion. The presented calculator gives the doctor the opportunity to identify a group of patients with the risk of rapid progression of CKD directly on an outpatient basis.

Loss characteristics and optimization method of a compressed air energy storage radial turbine with nozzle governing

During the operation of the compressed air energy storage (CAES) system, a discrepancy exists between the air storage pressure and the turbine inlet pressure. At the same time, to ensure that the turbine operates efficiently when the system load varies, the turbine needs to be regulated reasonably. In this paper, the influence of three nozzle governing (NG) parameters on turbine performance during the NG process is investigated: the inlet pressure of the NG region, the area of the NG region, and the base pressure. The flow characteristics and loss mechanisms under partial admission conditions and NG conditions are also analyzed. Furthermore, the NG process is optimized by using a transition section. The results show that the loss under the NG condition with low inlet pressure at the NG region is similar to the partial admission loss, both of which are mainly affected by the area of the NG region. In both working conditions, vortex structures appear at the stator outlet of the NG region. At the same time, the mixing of different airflows and the flow separation phenomenon within the rotor leads to a significant increase in entropy production rate. The transition section can attenuate the leakage and reduce the entropy production rate in the radial gap between the stator and rotor, increasing turbine efficiency by up to 1.1 % at maximum when using the transition section.

Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressures

This paper is devoted to studying structural stability of steady subsonic Euler flows in 2D finitely long nozzles. The reference flow is subsonic shear flows with general size of vorticity. The problem is described by the steady compressible Euler system. With admissible physical conditions and prescribed pressures at the entrances and the exits of the nozzles respectively, we establish unique existence and structural stability of this kind of subsonic shear flows. Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions, the problem is reformulated via Lagrange transformation and then decoupled into an elliptic mode and two hyperbolic modes. The elliptic mode is a mixed type boundary value problem of second order quasilinear elliptic equation for the stream function. The hyperbolic modes are transport types to control the total energy and the entropy. Mathematically, the iteration scheme is executed in a weight Hölder space with low regularity.

Predicting hospitalization costs for pulmonary tuberculosis patients based on machine learning

BackgroundPulmonary tuberculosis (PTB) is a prevalent chronic disease associated with a significant economic burden on patients. Using machine learning to predict hospitalization costs can allocate medical resources effectively and optimize the cost structure rationally, so as to control the hospitalization costs of patients better.MethodsThis research analyzed data (2020–2022) from a Kashgar pulmonary hospital’s information system, involving 9570 eligible PTB patients. SPSS 26.0 was used for multiple regression analysis, while Python 3.7 was used for random forest regression (RFR) and MLP. The training set included data from 2020 and 2021, while the test set included data from 2022. The models predicted seven various costs related to PTB patients, including diagnostic cost, medical service cost, material cost, treatment cost, drug cost, other cost, and total hospitalization cost. The model’s predictive performance was evaluated using R-square (R2), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE) metrics.ResultsAmong the 9570 PTB patients included in the study, the median and quartile of total hospitalization cost were 13,150.45 (9891.34, 19,648.48) yuan. Nine factors, including age, marital status, admission condition, length of hospital stay, initial treatment, presence of other diseases, transfer, drug resistance, and admission department, significantly influenced hospitalization costs for PTB patients. Overall, MLP demonstrated superior performance in most cost predictions, outperforming RFR and multiple regression; The performance of RFR is between MLP and multiple regression; The predictive performance of multiple regression is the lowest, but it shows the best results for Other costs.ConclusionThe MLP can effectively leverage patient information and accurately predict various hospitalization costs, achieving a rationalized structure of hospitalization costs by adjusting higher-cost inpatient items and balancing different cost categories. The insights of this predictive model also hold relevance for research in other medical conditions.

Fault signature extraction of rolling bearings under variable speed via time–frequency overlap group sparse representation

The high-fidelity extraction of the nonperiodic fault transients of rolling bearings under variable speed is of significant importance, while still a challenge for early-stage fault diagnosis of major equipment such as aero engines and wind turbines. A method termed continuous symmetric Laplace wavelet transform (CSLWT) enhanced time–frequency overlap group sparse (OGS) representation is proposed in this paper. A symmetric Laplace mother wavelet function is proposed which could satisfy the admissibility condition of wavelet decomposition and reconstruction, upon which the CSLWT is fabricated and adopted as the sparse representation dictionary to match the nonperiodic fault transients. Since the decomposition coefficients of nonperiodic fault impulses via the CSLWT exhibit group sparsity on the time–frequency plane with unknown intervals, the time–frequency OGS model is adopted and then solved for extraction of the nonperiodic fault transients. Moreover, a data driven, multi-objective optimization strategy is presented for determining the hyper-parameters of the sparse model. The correlated kurtosis of angular envelope signal (CK-AE) and harmonic-to-noise energy ratio of the order spectrum (HNR-OS) are introduced as the optimization objectives, and the Pareto front is solved based on the NSGA-II algorithm, upon which the acceptable solutions set is chosen from the Pareto front, and the proper hyper-parameters are further determined via proposed normalized solutions distance density sorting of the acceptable solutions set. The performance of the proposed method is validated via processing both simulated and experimental vibration signals, as well as compared with some tradition fault diagnosis methods.

ADMISSIBILITY OF EVIDENCE AS A FEATURE OF EVIDENCE IN CRIMINAL PROCEEDINGS

The institution of admissibility of evidence as a fundamental category of the criminal process has been discussed in the article. The author discussed issues such as the nature of evidence, its properties and conditions of admissibility in criminal proceedings. The author emphasizes that the admissibility of evidence not only protects the rights of participants in the process, but also affects the final court decision. Foreign experience and legislation were also studied and discussed.