Search Results (48)

By means of the weight functions, the idea of introduced parameters and the techniques of real analysis, we give a new reverse Hardy-type inequality and then obtain an extended reverse multidimensional half-discrete Hilbert-type inequality with the general homogeneous kernel and one partial sum. The equivalent statements of the best possible constant factor related to parameters, the equivalent forms and some particular examples are provided. Full article

This paper introduces a novel multidimensional half-discrete Hardy–Hilbert-type inequality that simultaneously addresses several key extensions in the literature. The inequality incorporates a general parameterized kernel involving a scalar term and the $\beta$-norm of a vector, and replaces the traditional discrete coefficient with a partial sum. Under suitable parameter conditions, the resulting inequality is sharper and preserves the optimal constant factor. The proof employs a systematic combination of weight-function techniques, parameter introduction, real-analysis methods, and the Euler–Maclaurin summation formula. Equivalent characterizations of the best possible constant are provided, and several meaningful corollaries are deduced, thereby unifying and generalizing a series of earlier inequalities. Full article

Alzheimer’s disease (AD) numbers among the most precipitative neurodegenerative disorders, constituting a constant subject of interest for medicinal chemistry researchers. The treatment of such disorders remains a challenge due to the complexity of their pathogenesis. Indeed, many factors are involved in the development of AD, including different enzymes such as acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), whose inhibition results in anti-AD activity, making the development of novel AChE/BuChE inhibitors a possible way to manage Alzheimer’s disease. Besides being a class of compounds with a wide spectrum of biological applications, acridine compounds also number among the most promising agents for the treatment of Alzheimer’s disease through cholinesterase inhibition. The best example to mention is the well-known anti-AD agent Tacrine. However, it was found to have a toxic effect on the liver, making the optimization of this acridine derivative a necessity. Our work was directed towards evaluating in silico a symmetrical acridine analogue as a potential cholinesterase inhibitor with controlled toxicity. A docking study was completed using Glide software (Schrodinger suites), and both AChE (pdb: 4EY6) and BuChE (4BDS) were utilized as drug targets. The molecular docking simulation resulted in satisfying docking score values alongside numerous significant interactions indicating the high stability of the investigated compound within the active sites of the enzymes studied. Additionally, ADMET prediction was carried out for the assessed acridine derivative in order to explore its drug likeness through its pharmacokinetics and toxicity profiles by employing the online servers SwissADME, MolSoft, and ProTox-II. Full article

In this paper, by introducing a general homogeneous kernel function and several parameters, we establish a new Hardy–Hilbert-type integral inequality involving two derivative functions of higher-order. For the resulting inequality, we determine the equivalent conditions of the best possible constant factor related to the parameters. As applications, we demonstrate that a lot of new Hardy–Hilbert-type integral inequalities can be derived by choosing specific homogeneous kernel functions. Full article

In this article, we study a directed version of Douglas–Rachford splitting method in real Hilbert spaces. By using new, self-contained, and simplified techniques, we prove its weak convergence. The major innovation is that we exploit the firm non-expansiveness of the Douglas–Rachford operator for the first time to derive the best possible upper bounds on direction factors, assuming that the involved factors remain constant. We give a new rare feature selection model equipped with the TripAdvisor hotel-review dataset. Numerical results confirm the user-friendliness and efficiency of directed Douglas–Rachford splitting in solving this model. Full article

In this paper, by using the techniques of real analysis, with the help of the Euler–Maclaurin summation formula, Abel’s summation by parts formula, and the differentiation mid-value theorem, we establish a half-discrete Hardy–Mulholland-type inequality involving one multiple upper limit function and one partial sum. Based on the obtained inequality, we characterize the condition of the best possible constant factor related to several parameters. At the end of the paper, we illustrate that some new half-discrete Hardy–Mulholland-type inequalities can be deduced from the special values of the parameters. Our results enrich the current results in the study of half-discrete Hardy–Mulholland-type inequalities. Full article

In this paper, by employing the Euler–Maclaurin summation formula and real analysis techniques, an improved version of the parameterized Hardy–Hilbert inequality involving two partial sums is established. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. Our results extend the classical Hardy–Hilbert inequality and improve certain existing results. Full article

In the initial part of this paper, we survey (in arbitrary spacetime dimension) the general FLRW cosmologies with non-interacting perfect fluids and with a canonical or phantom scalar field, minimally coupled to gravity and possibly self-interacting; after integrating the evolution equations for the fluids, any model of this kind can be described as a Lagrangian system with two degrees of freedom, where the Lagrange equations determine the evolution of the scale factor and the scalar field as functions of the cosmic time. We analyze specific solvable models, paying special attention to cases with a phantom scalar; the latter favors the emergence of nonsingular cosmologies in which the Big Bang is replaced, e.g., with a Big Bounce or a periodic behavior. As a first example, we consider the case with dust (i.e., pressureless matter), radiation, and a scalar field with a constant self-interaction potential (this is equivalent to a model with dust, radiation, a free scalar field and a cosmological constant in the Einstein equations). In the phantom subcase (say, with nonpositive spatial curvature), this yields a Big Bounce cosmology, which is a non-absurd alternative to the standard ($\Lambda$CDM) Big Bang cosmology; this Big Bounce model is analyzed in detail, even from a quantitative viewpoint. We subsequently consider a class of cosmological models with dust and a phantom scalar, whose self-potential has a special trigonometric form. The Lagrange equations for these models are decoupled passing to suitable coordinates $(x,y)$, which can be interpreted geometrically as Cartesian coordinates in a Euclidean plane: in this description, the scale factor is a power of the radius $r=\sqrt{x^2+y^2}$. Each one of the coordinates $x,y$ evolves like a harmonic repulsor, a harmonic oscillator, or a free particle (depending on the signs of certain constants in the self-interaction potential of the phantom scalar). In particular, in the case of two harmonic oscillators, the curves in the plane described by the point $(x,y)$ as a function of time are the Lissajous curves, well known in other settings but not so popular in cosmology. A general comparison is performed between the contents of the present work and the previous literature on FLRW cosmological models with scalar fields, to the best of our knowledge. Full article

In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to the parameters and deal with the equivalent inequalities. Our main result provided a new generalization of Hardy–Littlewood–Polya inequality, and as a consequence, we show that some new inequalities of the Hardy–Littlewood–Polya type can be derived from the current results by taking the special values of parameters. Full article

In the context of the development of technologies, every sports club tends to improve its training methods to obtain the best possible results in sports training. The goal of the research is to develop a specialized training program designed to enhance ball-control skills so that children can play soccer with increased confidence, therefore reinforcing their need for constant visual contact with the ball during possession. The study participants are children between the ages of 8 and 10, who have acquired at least one year of consistent and well-structured football practice, divided into two groups, experimental group I and control group II. The T-Blaze test training, the Adams test, and the registration of the degree of head tilt using artificial intelligence and visual recognition were implemented. During the training, the authors used the BlazePod sensors to measure participants’ times more precisely, thus avoiding the inaccuracy of using a classic timer. At the same time, the authors used the Vesta HeadUp to block the child’s view of the ball when he has possession of the ball or is very close to it. The recording of time spent playing head-up and head-down revealed statistically significant differences between the three test sessions in favor of the experimental group. Considering the statistically substantial influence obtained, the authors can conclude that our intervention program based on specific means and using HeadUp vests was a decisive factor in achieving improved performance. Full article

Breast cancer (BC) is the most common type of cancer in women and the number of new cases in the US is still increasing each year. Triple-negative breast cancer (TNBC), which comprises 15–20% of all breast cancer, is a heterogeneous disease and is considered the most aggressive type of breast cancer due to the lack of estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2) expressions for treatments. Traditional chemotherapy is the standard protocol for the treatment of TNBC. Toxicity and multidrug resistance are major drawbacks to chemotherapy. The lack of molecular targets and poor prognosis for TNBC prompts an urgent need to discover novel therapeutic strategies to improve clinical outcomes and quality of life for patients. Photodynamic therapy (PDT) or light treatment is a binary anti-cancer procedure that uses a photosensitizer (PS) that, upon light activation, produces cytotoxic oxygen species, destroying tumor cells. PDT is minimally invasive and can be repeated a few times without accumulating significant toxicity in the surrounding tissues. The primary goal of this study was to investigate in vitro photodynamic chemotherapy as a ternary combination therapy using our synthesized photosensitizers (chlorin–vitamin conjugates and their corresponding indium complexes) co-treated with known chemotherapeutic agents (taxol, doxorubicin, cisplatin, fluorouracil, or methotrexate) in the presence of light and determine the optimum conditions as a pre-clinical study of an enhanced tumoricidal effect against TNBC. Our results indicated that the best combination for an effective chemophotodynamic effect involves a ternary treatment of the indium complex of the chlorin–lipoic acid conjugate (InCLA) co-treated with taxol, which exhibited strong synergism at the nanomolar concentration when combined in the presence of visible light irradiation. Other ternary combinations containing taxol with a synergistic anti-tumor effect against TNBC include chlorin–pantothenic acid (CPA) and chlorin–biotin (CBTN) conjugates. Several other ternary combinations containing InCLA, CBTN, and CPA with either cisplatin, fluorouracil, or methotrexate were identified to generate a synergistic or additive effect. The light dosage remained constant, but the dosages of photosensitizers and chemotherapy drugs were varied to obtain the lowest possible concentration for the desired effect. The synergistic, additive or antagonistic effects of the drug combinations were determined based on the Chou–Talalay method, with InCLA–taxol having the lowest combination index (CI) of 0.25. Fluorescence and transmission electron microscopy (TEM) images provided evidence of apoptosis as the preferred mode of cell death. Our study demonstrated the combination of PDT and chemotherapy as a potential treatment option for TNBC patients. Full article

The recovery of the grain matrix from spent moulding sand is a constant challenge in making the best possible use of the deposits of quartz sand material, as well as in protecting them. In the case of spent sand with organic binders, the best method to recover the grain matrix is thermal regeneration. However, this method is expensive and requires adequate attention to the emission of harmful compounds into the atmosphere. This paper presents a new concept for implementing the thermal regeneration process. A suitable regeneration temperature was adopted for the furfuryl binder moulding sand, and a change in the design of the device was introduced in the area of the utilisation of gases generated during the combustion of the spent binder. To confirm the assumptions made, and to assess the appropriate suitability of the material recovered, the technological parameters of the material obtained were verified, namely, ignition losses, sieve analysis, bending strength, and pH value. The consumption of media for the process was also analysed from an economic point of view, as well as the emission of BTEX (a mixture of volatile aromatic hydrocarbons-benzene, toluene and three isomers of xylene) gases under different conditions of the process. On the basis of the research conducted, it was concluded that lowering the regeneration temperature of regeneration does not adversely affect the technological parameters of the moulding sand on the regenerate matrix. Changing the design of the regenerator does not result in increased emissions of harmful substances to the environment. Studies indicate that the appropriate setting of thermal regeneration parameters and the optimal design of the employed equipment are favourable factors in reducing the cost of the process while not compromising the quality of the moulding sand and the environmental impact. Full article

The growth in the demand for electrical energy, which is driven by the constant growth of the metropolises and the expansion of the productive capacities of the industrial sector, entails the inevitable development of the electrical system to satisfy all the required demands in a convenient, efficient, and reliable manner. In this scenario, power distribution companies will continue to need to expand their electrical systems in the short and medium term to obtain the lowest investment and operating prices for the period considered in the analysis horizon. The expansion of the system can be projected statically or dynamically, which depends on the criteria that each distributor, in turn, applies in their expansion projects. Multi-criteria decision making can provide deeper analysis perspectives considering infinite possibilities for optimal network sizing and the technical, operational, quality of service, and even system reliability factors. This research proposes a multi-criteria decision technique based on the CRITIC method to determine the optimal design of an electrical distribution system. For this purpose, several design scenarios are defined with different types of electrical conductors, and the power flows are calculated in each. From these simulations, the results obtained in voltage profiles, namely active and reactive power losses, current levels, and the costs associated with the conductors used, are recorded. With the multi-criteria technique, the winning alternative is the design scenario containing the best joint solutions for the analysis variables. The proposed methodology is validated in an IEEE 34-bar test system. The Matpower tool, available through Matlab, generates power flows for each proposed design case. The results obtained in the analysis variables are generated and stored in a decision matrix of 210 alternatives. The proposed method represents a novel and powerful alternative for design proposals of distribution systems considering quality, efficiency, and cost criteria. Full article

By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as $H(||x|{|}_{\alpha }^{{\lambda }_1}||y|{|}_{\beta }^{{\lambda }_2})$$({\lambda }_1,{\lambda }_2\ne 0)$ are given, which are some extensions of the Hilbert-type integral inequalities in the two-dimensional case. Some equivalent conditions of the best value and several parameters related to the new inequalities are provided. Two corollaries regarding the kernel, represented as $k_{\lambda }{(||x|{|}_{\alpha }^{{\lambda }_1},||y|{|}_{\beta }^{{\lambda }_2})}^{}({\lambda }_1,{\lambda }_2\ne 0)$, are given, and a few new inequalities for the particular parameters are obtained. Full article

In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial summation formula, and differential mean value theorem, a new weighted Hardy–Hilbert-type inequality containing two partial sums can be proven, which is a further generalization of an existing result. Based on the obtained results, we provide the equivalent statements of the best possible constant factor related to several parameters. Also, we illustrate how the inequalities obtained in the main results can generate some new Hardy–Hilbert-type inequalities. Full article