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ISSN: 2523-0212 (online) 2616-4906 (Print)
ISSN: 2616-8111 (online) 2616-8103 (Print)
ISSN: 2617-9687 (online) 2617-9679 (Print)
ISSN: 2618-0758 (online) 2618-074X (Print)
ISSN: 2617-9709 (online) 2617-9695 (Print)
ISSN: 2791-0814 (online) 2791-0806 (Print)
Open Journal of Mathematical Sciences (OMS)
ISSN: 2523-0212 (online) 2616-4906 (Print)
Open Journal of Mathematical Analysis (OMA)
ISSN: 2616-8111 (online) 2616-8103 (Print)
Open Journal of Discrete Applied Mathematics (ODAM)
ISSN: 2617-9687 (online) 2617-9679 (Print)
Ptolemy Journal of Chemistry (PJC)
ISSN: 2618-0758 (online) 2618-074X (Print)
Engineering and Applied Science Letters (EASL)
ISSN: 2617-9709 (online) 2617-9695 (Print)
Trends in Clinical and Medical Sciences (TCMS)
ISSN: 2791-0814 (online) 2791-0806 (Print)
We introduce Littlewood Paley functions defined in terms of a reparameterization of the Ornstein-Uhlenbeck semigroup obtaining that these operators are bounded in \(L^p\), \(1<p<\infty\), with respect to the unidimensional gaussian measure, by means of singular integrals theory. In addition, we study the Abel summability of the Fourier Hermite expansions considering their pointwise convergence and their convergence in the \(L^p\) sense, obtaining a version of Tauber’s theorem.
A series of novel 2-methyl-5-[2-(substituted)phenyl]-1,3,4-oxadiazole derivatives (6a–6i) was synthesized via a multi-step protocol starting from commercially available salicylic acid (1). The initial esterification of salicylic acid using thionyl chloride and ethanol at 80 °C for 12 h yielded ethyl 2-hydroxybenzoate (2), which was subsequently converted to 2-hydroxybenzohydrazide (3) upon treatment with hydrazine monohydrate in ethanol at 80 °C for 2 h. Acetylation of intermediate 3 with acetic anhydride afforded N’-acetyl-2-hydroxybenzoate (4), which was reacted with various halo compounds (4a–4i) to produce a series of N’-acetyl-2-(substituted)oxybenzohydrazides (5a–5i). These key intermediates were cyclized using triphenylphosphine, triethylamine, carbon tetrachloride, and acetonitrile at 100 °C for 1 h to furnish the final oxadiazole derivatives (6a–6i). The compounds were purified using appropriate chromatographic techniques and fully characterized by 1H NMR, 13C NMR, FTIR, and mass spectrometry. Biological screening of the synthesized compounds revealed that several derivatives, particularly 6c, 6d, and 6g, exhibited promising antimicrobial and antioxidant activities. Notably, compound 6a demonstrated significant cytotoxicity against HeLa cancer cells. Molecular docking studies further supported the biological potential of the compounds, with 6e displaying a high docking score of –5.66 kcal/mol.
Shea butter is a natural moisturizer used to improve skin health. This study investigates its effects on skin barrier function, hy-dration, and lipid profile, using analytical chemistry methodologies. Trans-Epithelial Water Loss (TEWL), corneometry, im-pedance spectroscopy, and gas chromatography-mass spectrometry (GC-MS) were used to assess skin barrier function, hydra-tion, and lipid profile after shea butter application. Results show that TEWL decreased by 37.8% after 24 hours (p < 0.01), Skin hydration increased by 58% after 24 hours (p< 0.001). Impedance spectroscopy showed a 33% increase in skin imped-ance, GC-MS analysis revealed a balanced fatty acid composition in shea butter, ceramide profiling showed six subclasses, with Ceramide 1 and 2 being the most abundant. The results demonstrate shea butter's efficacy in improving skin barrier func-tion, hydration, and lipid profile. The rapid decrease in TEWL and increase in skin hydration suggest immediate effects on skin lipids. Shea butter's fatty acid composition contributes to its moisturizing and barrier-enhancing properties. This study provides evidence for the benefits of shea butter in maintaining healthy skin. Its natural moisturizing properties make it a valuable in-gredient in skincare products.
Urbanization and soil degradation have placed significant pressure on agricultural sustainability and food security, prompting the exploration of alternatives to soil. The potential of corncob as soilless substrate, an innovative growing media for sustainable urban agriculture, has been preliminary established. Hence, this study investigated the design-related properties of corncob necessary for developing crusher for producing corncob substrate using standard methods. Corncobs from yellow and white corn varieties were used for the study at five moisture levels (9.71, 11.01, 14.29, 17.58 and 21.87% w.b). The results indicate that moisture content rise increased the major axes, angle of repose, surface area and static coefficient of friction. Sphericity decreased for yellow corncob from 0.50 to 0.47 but increased for white corncob from 0.63 to 0.65. Solid and bulk densities decreased: yellow corncob from 0.365 to 0.290 g/cm³ and 0.325 to 0.225 g/cm³, respectively; white corncob from 0.395 to 0.340 g/cm³ and 0.345 to 0.270 g/cm³, respectively. Rupture strengths decreased from 1.12 to 0.80 N/mm² and 1.12 to 0.80 N/mm² for yellow and white corncobs, respectively. Valorization of corncob will create new economic opportunities and give farmers more value for their corn. Hence, this work is pivotal in achieving that with the empirical data provided for developing a corncob crusher for soilless substrate production.
Herein we have discussed various microscopic techniques for analysis of nanomaterials and biomaterials. We have discussed the origin of concept of magnification and resolution. The first attempt of magnification was done with the help of lenses. Thus, we have discussed various types of lenses and their properties. Then after various progress has taken place in the domain of magnification and today we are gifted with advanced microscopes. In this review article we have tried to classify the microscopic techniques into different categories as optical microscopes and acoustic microscopes. Also we have discussed the subtypes of optical microscope like simple microscope, compound microscope, Raman microscope, UV Visible microscope, Dark Field Microscope, Bright Field Microscope etc. Here we have discussed the historical aspects of developments in the microscopic techniques starting from the lens to the advanced Microscopic techniques etc. We have discussed the developmental stage, discovery of each microscope and then we discussed working principle of the instrument, its applications and advantages and limitations too. This review paper is useful for the researchers working in veterinary medicine, microbiology, health sciences, nanoscience and technology etc.
Dowsing experimental technique (DET), also known as divination, has been used to serve human needs across different civilizations. A comprehensive review of the literature on DET indicates that scientists are divided into two groups, regarding DET’s science and interpretation. One group believes that there is pure physics and chemistry behind DET and, therefore, it should be considered as one of the applied sciences used for materials’ prospecting. The other group believes that identification of materials using DET can be explained as a psychological behavior. In this research paper, DET has been used to identify several materials, and the various possible mechanisms behind it also examined. Accordingly, 68 samples were collected from various locations in Jordan and Palestine to identify them using DET. The collected samples, including different kinds of minerals, metals, rocks, etc., were divided into 9 groups. Experiments were conducted on combinations of the collected materials, using wooden rods and two capsules filled with crushed materials and placed on the rods. It is believed that the materials were identified using DET because of energy radiation, thermal conduction, piezoelectric effects, and/or electrostatic forces. DET may be also interpreted in terms of psychological perspectives, as being a psychological kinesthetic sense. So that these forces may be able to move the rods towards the target material, identify it, and recognize its location. However, DET is still an open question for further research, including cyber-psychology and other digital tools. In short, DET has proven to be a successful, easy, cheap, applicable, and sustainable technique for identifying and locating various materials.
The main focus of this paper is to define the Wigner transform on Chébli-Trimèche hypergroups of exponential growth and to present several related results. Next, we introduce a new class of pseudo-differential operators ℒψ1, ψ2(σ), called localization operators, which depend on a symbol σ and two admissible functions ψ1 and ψ2. We provide criteria, in terms of the symbol σ, for their boundedness and compactness. We also show that these operators belong to the Schatten–von Neumann class Sp for all p ∈ [1, +∞], and we derive a trace formula.
The exact deg-centric graph of a simple graph \(G\), denoted by \(G_{ed}\), is a graph constructed from \(G\) such that \(V(G_{ed}) = V(G)\) and \(E(G_{ed}) = \{v_iv_j: d_G(v_i,v_j) = deg_G(v_i)\}\). This research note presents the domination numbers of both the Jaco graph \(J_n(x)\) and the exact deg-centric graph of the family of Jaco graphs. The respective complement graphs are also addressed.
The first Zagreb index of a graph is one of the most important topological indices in chemical graph theory. It is also an important invariant of general graphs. The first Zagreb index of a graph is defined as the sum of the squares of the degrees of the vertices in the graph. The research on the Hamiltonian properties of a graph is an important topic in graph theory. Use the Diaz-Metcalf inequality, we in this paper present new sufficient conditions based on the first Zagreb index for the Hamiltonian and traceable graphs. In addition, using the ideas of obtaining the sufficient conditions, we also present an upper bound for the first Zagreb index of a graph. The graphs achieving the upper bound are also characterized.
A Young subgroup of the symmetric group \(\mathcal{S}_{N}\) with three factors, is realized as the stabilizer \(G_{n}\) of a monomial \(x^{\lambda}\) ( \(=x_{1}^{\lambda_{1}}x_{2}^{\lambda_{2} }\cdots x_{N}^{\lambda_{N}}\)) with \(\lambda=\left( d_{1}^{n_{1}},d_{2}^{n_{2}},d_{3}^{n_{3}}\right)\) (meaning \(d_{j}\) is repeated \(n_{j}\) times, \(1\leq j\leq3\)), thus is isomorphic to the direct product \(\mathcal{S}_{n_{1}}\times\mathcal{S}_{n_{2}}\times\mathcal{S}_{n_{3}}\). The orbit of \(x^{\lambda}\) under the action of \(\mathcal{S}_{N}\) (by permutation of coordinates) spans a module \(V_{\lambda}\), the representation induced from the identity representation of \(G_{n}\). The space \(V_{\lambda}\) decomposes into a direct sum of irreducible \(\mathcal{S}_{N}\)-modules. The spherical function is defined for each of these, it is the character of the module averaged over the group \(G_{n}\). This paper concerns the value of certain spherical functions evaluated at a cycle which has no more than one entry in each of the three intervals \(I_{j}=\left\{ i:\lambda_{i}=d_{j}\right\} ,1\leq j\leq3\). These values appear in the study of eigenvalues of the Heckman-Polychronakos operators in the paper by V. Gorin and the author (arXiv:2412:01938v1). The present paper determines the spherical function values for \(\mathcal{S}_{N}\)-modules \(V\) of two-row tableau type, corresponding to Young tableaux of shape \(\left[ N-k,k\right]\). The method is based on analyzing the effect of a cycle on \(G_{n}\)-invariant elements of \(V\). These are constructed in terms of Hahn polynomials in two variables.
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