In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

The study aimed to estimate the prevalence and associated factors of cervical and breast cancer screening among women in the general population in Jordan. Nationally representative cross-sectional data were analysed from 14,689 women (34 years median age, range 15-49) that took part in the “2017-18 Jordan Population and Family Health Survey”. Information about cancer screening uptake included Pap smear, clinical breast examination, and mammography. Results indicate that the prevalence of ever Pap smear cancer screening was 15.3%, clinical breast examination in the past 12 months 13.9% and ever mammography 8.7%. In adjusted logistic regression analysis, older age, higher wealth, greater media exposure and tobacco use were positively and being Syrian, and living in the southern region were negatively associated with ever Pap smear, clinical breast examination in the past 12 months, and ever mammography. In addition, high decision-making power was associated with the uptake of Pap smear and higher education was associated with ever mammography. The study showed a low cancer screening uptake, and several factors were identified that can assist in promoting cancer screening in Jordan.

This study finds that in northern Jordan, breeder indicators present challenges to the sustainability and growth of sheep and goat farming, while economic indicators suggest a combination of financial stability alongside hurdles related to profitability and resource ownership. Breeder age plays a role in the management of livestock herds, due to factors such as experience, resources, or adherence to traditional practices. Experience significantly affects breeders' decisions on male insemination replacements, likely due to skill. Crop cultivation influences breeders' returns by reducing feeding costs, while strategic lamb sales management boosts individual animal profitability. Winter raises animal mortality due to cold stress. Other animals in herds increase kid mortality by spreading diseases. Breeder experience significantly affects lamb survival, stressing its role in care. Increasing sheep proportion enhances lamb production and reduces lamb mortality while managing rams and selling lambs positively affects herd health and productivity. A larger goat herd proportion positively correlates with kids sold but inversely with breeding males and overall kids, implying trade-offs affecting herd productivity and mortality rates. Sheep herds (92.5%) show slightly better reproductive success than goats (90.6%), implying superior long-term viability. Flock excels in birth, survival, and sales, but low sheep and lamb%. Improvement is needed for sustainability, and the potential is high. Goat breeding shines in birth, sales, and overall success, but needs attention to kid survival and other sustainability issues. In conclusion, despite challenges, there are promising opportunities to enhance sheep and goat farming in Jordan. Effective management, informed by breeders' experience and economics, is crucial. Empowering small-scale herders and implementing targeted interventions like winter mortality solutions and selective breeding is vital for sustainable growth.

This study aimed to assess the ability of community pharmacists to recognize cases of Loperamide abuse at the point of sale, their perspective of and experience towards potential abuse cases. Methods: A cross-sectional study was conducted in Jordan, using a self-administered online questionnaire. The questionnaire consisted of 3 main parts: demographics, the experience of pharmacists with abusers' behavior, as well as their perspectives towards Loperamide abuse. Results: A total of 250 community pharmacists completed the survey, 54% (135) of which were female. Almost one-third (33.2%; 83) of the participants reported exposure to suspected cases of Loperamide abuse during the last six months. Pharmacists declared that most of the suspected Loperamide abusers were male (60.2%), of middle-low socioeconomic status (69.9%), and between 20-30 years of age (57.8%). The largest quantity (packs) of Loperamide requested by a single patient was around 33.2±14.9 at once. As reported by pharmacists, the suspected reasons behind Loperamide abuse included 50% seeking euphoria, 17% relieving anxiety, and 33% controlling addiction (weaning off other opioids). The multivariate logistic regression analysis demonstrated a significant correlation between male gender (OR=1.2, 95% CI 0.12-1.59), pharmacy location in the center of Jordan (OR=21.2, 95%CI 2.45-183.59), late-night working shift (Shift C, OR=1.29, 95% CI 0.12-2.08) and abuse to Loperamide during the last six months. Conclusion: This study shed light on Loperamide abuse which is highly influenced by different sociodemographic characteristics. Accordingly, close monitoring and thorough tackling of the abuse practices are mandated through an increase in educational and awareness campaigns about proper medication use.

This review provides an understanding of the teaching and practising of forensic accounting across the globe. It includes a review of published forensic accounting studies that conclude that forensic accounting is of benefit to both students and professionals. Despite this, there are areas of concern; namely, the insufficiency of an appropriate structure of regulation and a lack of control over the academic qualifications to enter the profession. This review of both the teaching and practising of forensic accounting provides an overview of the vital issues and concerns that must be understood in order to advance the essential application of forensic accounting. It is expected that this review will influence future policy that will advance business and limit episodes of fraud. The amount of published literature on the subject of forensic accounting is widespread and diverse. However, there is a lack of comprehensive understanding regarding the strengths and weaknesses of forensic accounting; this review will address this and provide policymakers with a thorough explanation of the subject.

We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born--Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

Background: Regardless of the indisputable benefits of insulin therapy, initiating insulin for diagnosed children with diabetes might be intimidating for parents. This study assesses the experience, fears, barriers and adherence to insulin use among the parents of diagnosed children with diabetes. Methods: A cross-sectional online survey was utilized for data collection from 218 participants between February and March 2023 in Jordan. The survey consisted of six sections to evaluate and assess: sociodemographic for both children with diabetes and their parents, the experience of using the insulin, the diabetes fear of self-injecting questionnaire (D-FISQ), the barriers for insulin administration including both sociocultural and other insulin-related factors, and insulin adherence. Results: More than 80% of the participants perceived a number of sociocultural barriers to insulin administration such as the tendency for addiction, lower efficiency of insulin than oral medication, and preference for complementary medicine over insulin. More than two-thirds of the participants complained of insulin-related barriers such as infections and sudden death in addition to learning the correct injection method. The general fear level was low, 8.56±7.87 (out of 45); however, more fear of insulin injection and self-testing was significantly associated with both sociocultural and insulin-related barriers, especially at the younger age. Conclusion: The results of this study indicated that parents have several barriers to insulin administration, mainly related to insulin injection. Therefore, more awareness about insulin therapy can help adjust the cooperation of patients, acceptance of treatment, ending with improving the quality of life and well-being.

The World Health Organization estimated that around 66 thousand HBV are caused by needlestick injuries annually. Healthcare students should be aware of HBV transmission route and preventive measures. This study assessed the knowledge, attitudes, and practices toward HBV among Jordanian healthcare students and its associated factor. A cross-national study conducted from March to August. The participants were asked to complete the questionnaire. It had four sections: participants' sociodemographic, knowledge, attitudes, and practices about HBV. 2322 participants were enrolled, 67.9% were females, 26.4% were medical student, 35.9% were in the 3rd year. 40% of the participants held a high level of knowledge and attitude. 63.9% of participants had good practices toward HBV. Medical students in the last year of study, encountered HBV patients , had better knowledge. Male students from medicine college, encountered HBV patients and had extra HBV courses showed better attitude. High practice level was associated with being dentistry student, at 5th year, encountered HBV patient and extras HBV courses. This study demonstrated insufficient knowledge and attitudes toward HBV, the practices level toward HBV among healthcare students was promising. Subsequently, public health efforts should modify the knowledge and attitude gaps to reinforce awareness and minimizing risks of the infection.

Despite the scientific and technological development, libraries of Jordanian universities suffer from an obvious lack of digital information resources, because for many reasons, the most important of these is the non-application of intellectual property legislation (IPL) related to these resources. This study investigated the reality of the application of intellectual property legislation related to digital information resources at the libraries of public universities in Jordan. The population study consisted of all employees of departments of digital information resources. The study sample was (74) employees. Texts of regulations for the intended libraries and the Jordanian copyright law No. (22) for the year (1992) were reviewed and analyzed. In addition, a questionnaire was developed regarding the actual application of intellectual property legislation relating to digital resources at the university libraries in Jordan. Results revealed that the application of IP legislation relating to digital resources at the libraries of public universities in Jordan was moderate and that the supervising to the libraries of universities from the National Library regarding the protection of intellectual property rights of digital resources was moderate. The study recommended the application of intellectual property legislation related to digital resources in the intended libraries, this could be achieved through including intellectual property legislation in the regulations of public services in the intended libraries, to provide for the terms of protecting IP rights for digital resources, improving the legislation, developing of the Jordanian copyright law to be compatible with digital information resources, providing the necessary support for these libraries, and emphasizing the role of the National Library.

Presently, Jordan confronts a double substantial challenge of enhancing energy security and mitigating greenhouse gas emissions. One of the most encouraging avenues to attain the objectives of sustainable development, energy security, and environmental conservation is to enhance the integration of renewable energy into the generation of electricity. In pursuit of this goal, the Jordanian government intends to expand investments in the green energy sector, with solar and wind energy poised to play a key role in satisfying energy demands and cultivating an environmental sustainability. This paper aims to examine the distinctive dynamics, challenges, obstacles, and potential solutions corresponding to the establishment of community solar and wind farms in Jordan suburban areas. It aims to highlight the opportunities and barriers influencing the track of sustainable energy adoption in the country. Through a comprehensive analysis of the Jordanian context, the goal is to extract insights that can guide policies and practices. Additionally, the findings may serve as a valuable benchmark for other regions confronting similar challenges on their pursuit for a sustainable energy future.

Introduction. Streptococcus pneumoniae infections are a major cause of mortality and morbidity worldwide. In Jordan, pneumococcal conjugate vaccines (PCVs) are not included in the national vaccination program. Due to the current availability of several PCVs including PCV-10, PCV-13 and PCV-15, along with PCV-20, currently undergoing pediatric approvals globally, the decision to introduce PCVs and their selection should be based on valid local data on the common serotypes of Streptococcus pneumoniae. Methods: This cross-sectional study aimed to identify the frequency of serotypes of Streptococcus pneumoniae in children aged below 5 years hospitalized with invasive pneumococcal diseases (IPD) including pneumonia, septicemia and meningitis during the study’s duration in representative areas of Jordan. Serotyping for culture-positive cases was based on the capsular reaction test, known as the Quellung reaction. qPCR was conducted on blood samples of patients with lobar pneumonia identified via X-ray or on cerebrospinal fluid for those with a positive latex agglutination test for Streptococcus pneumoniae. Results. This study was based on the analysis of the serotypes of 1015 Streptococcus pneumoniae cases among children younger than the age of 5; 1006 cases with pneumonia, 6 cases with meningitis, and 3 cases with septicemia. Only 23 culture-positive cases were identified, in comparison to 992 lobar pneumonia cases which were PCR-positive but culture-negative, with a PCR positivity rate of 92%. Serotypes 6B, 6A, 14 and 19F were the most common serotypes identified in the study, with prevalence rates of 16.45%, 13.60%, 12.12% and 8.18%, respectively. PCV-10, PCV-13, PCV-15 and PCV-20 coverage rates were 45.32%, 61.87%, 64.14% and 68.47%, respectively. Discussion: To the best of our knowledge, this is largest prospective study from the Middle East and one of the largest studies worldwide showing the serotypes of Streptococcus pneumoniae. It reveals the urgency for the introduction of PCV vaccination in Jordan, utilizing recently developed vaccines with broader serotype coverage.

We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are yikx=αikx+βik i,k=1...6, αik≠0. We color the edges connecting the points for which αik>0 holds with red, and the edges for which αik<0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R3,3=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.

Customs law and procedures are important part of the trade system in Jordan. They regulate the flow of goods across the borders. The purpose of this paper is to examine Jordan's import regime by analyzing customs law, rules of origin, free trade zones, and tariffs reform.

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

Psychiatric nurses were challenged with high levels of stress, which in turn lower their professional quality of life (ProQoL) and job satisfaction and increase their intention to leave job at psychiatric settings. Adequate level of ProQoL improve patient care provision. The purpose is to assess the levels, relationships, and predictors of professional quality of life of Jordanian psychiatric nurses and their job satisfaction and intention to leave job. A descriptive cross-sectional design was used to collect data using the Professional Quality of Life Scale-5 from a convenience sample of 144 psychiatric nurses. Results showed that the mean score of compassion satisfaction (CS), burnout (BO), and secondary traumatic stress (STS) were 35.21, 27.0, and 26.36, respectively. The mean scores of intention to leave and job satisfaction were 2.33, and 3.7, respectively. Income level, educational level, intention to leave, and job satisfaction were significantly differing in CS dimension. Nurses’ age, intention to leave, and job satisfaction were significantly differing in BO. Nurses’ age, years of experience, frequent C-shift worked, and work affiliation were different in STS. Burnout, STS, and educational level predicted CS. CS, STS, job satisfaction, and level of education predicted BO. BO, CS, and frequent working night C-shift predicted STS. More studies are needed to assess the factors that affect ProQoL among psychiatric nurses, and to evaluate interventional programs that improve quality of life of psychiatric nurses. This is important in retaining nurses and increasing their job satisfaction. Jordanian psychiatric nurses reported moderate level of (ProQoL), high level of job satisfaction, and low intention to leave job. There is a need to enhance (ProQoL).

The Center for Disease Control and Prevention and the World Health Organization issued a practical approach and Global Action Plan to control the threatening emerging antibacterial resistance. One of the main basis of this plan is the Antimicrobial Stewardship Program (ASPs). This study aimed to evaluate community pharmacists’ awareness and perception towards antimicrobial resistance and ASPs in Jordan. Thus, a qualitative study was conducted through in-depth interviews with twenty community pharmacists. Convienience sampling was used in the study. Qualitative analysis of the data yielded four themes and eleven sub-themes. All the respondents showed good understanding about the causes of antimicrobial resistance. The most important causes reported by them was the non-restricted prescription of antimicrobials. Most of the pharmacists believed that they are competent to provide ASPs, however, they believed that there are several barriers against the implementation of ASPs in community pharmacies in Jordan. Barriers demonstrated by the pharmacists, including organizational obstacles, resources obstacles, and personal obstacles. As a conclusion, this study revealed several barriers against the implementation of ASPs in community pharmacies in Jordan. Incorporating ASPs in the community pharmacy settings requires proper pharmacist training, several academic disciplines team efforts, and good pharmacy practice of antimicrobial guidelines.

This paper is based on a talk given at the 14-th International Workshop on Differential Geometry and Its Applications, hosted by the Petroleum Gas University from Ploiesti, between July 9-th and July 11-th, 2019. After presenting some historical facts, we will consider some geometry problems related to unification approaches. Jordan algebras and Lie algebras are the main non-associative structures. Attempts to unify non-associative algebras and associative algebras led to UJLA structures. Another algebraic structure which unifies non-associative algebras and associative algebras is the Yang-Baxter equation. We will review topics relared to the Yang-Baxter equation and Yang-Baxter systems, with the goal to unify constructions from Differential Geometry.

The outbreak of coronavirus 2 (SARS-CoV-2) has already taken on pandemic proportions and has affected more than 100 countries in recent weeks. It is imperative that global healthcare systems are prepared. Containment initiatives in Jordan, on the other hand, have decreased new cases by over 63%. The Jordanian national health system has been very pleased with its ability to adequately meet the needs of the patients diagnosed with SARS-CoV-2 pneumonia, and includes intensive care. From 2 March to 14 April 2020, between 4% and 8% of active infected patients in Jordan registered daily in intensive care. The percentage is very low.

Corporate governance is developing rapidly in many countries across the world. In this article, the existing state of corporate governance in Jordan is examined. Jordan does not have a corporate governance code per se. The article reveals that overall Jordan has in place some of the features of corporate governance best practice, but that there remains further progress to be made in areas such as independence of directors, compensation, and correlation between shareholding and entitlement to seats on the board. The article recommends legal reforms in order to enhance corporate governance in Jordan.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

Although vaccinating the world is adopted by the WHO to limit COVID-19 transmission, people’s worries about vaccines may suppress their desire for vaccination despite vaccine availability. This study aimed to evaluate the levels of stress and anxiety among 250 Jordanians who received their first vaccine dose at a local community health center. The respondents completed the stress and anxiety subscales of the Depression Anxiety and Stress scale 21 (DASS-21) pre- and post-vaccination. The respondents expressed more moderate-severe levels of stress pre than post vaccination (20.8% and 13.2%, respectively). Meanwhile, 37.2% and 45.2% of the respondents expressed moderate-severe anxiety pre and post vaccination, respectively. Wilcoxon signed-rank test revealed that the drop in the level of stress from pre (median (IQR) = 5 (1-8)) to post vaccination (median (IQR) = 3 (1-7)) was statistically significant (z = -3.81, p = 0.001, r = 0.17) while the increase in anxiety was not. Anxiety median significantly dropped among individuals experiencing mild to severe anxiety pre vaccination. Similarly, stress and anxiety significantly increased among individuals expressing normal anxiety pre vaccination (z = -3.57 and -8.24, p values = 0.001, r = 0.16 and 0.37, respectively). Age positively correlated with post vaccination anxiety among respondents with mild pre vaccination anxiety, and it negatively correlated with pre vaccination level of stress in the normal anxiety group. Gender, marital status, respondents’ level of education, and history of COVID-19 infection had no significant correlation with anxiety or stress at either point of measurement. Overcoming their hesitancy to receive COVID-19 vaccine, individuals with normal levels of anxiety experienced a rise in their distress symptoms following immunization. On the contrary, vaccination seemed to desensitize anxious individuals. Policymakers need to formulate a population-specific plan to increase vaccine preparedness and promote psychological well-being over all during the pandemic.

Snap-fit is a commonly used jointing/connention mechanism, and its easy installation and difficult removal are the result of the coordinated interaction between friction, geometric shape, and elasticity. This paper presents a detailed study on the assembly/disassembly forces of thin-walled torus snap-fit through finite element simulation, experimental testing, and data fitting of approximate analytical solutions. The research reveals that the non-zero Gaussian curvature of the torus has a significant impact on the mechanical performance of the torus snap fit. The findings in this study are of great significance for future design of high-performance structural connections.

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

In this work, we explore a the different forms of a new type of modified gravity, namely f(φ) gravity. We construct the Big Rip type for the energy density and the curvature of the universe. We show that dark energy is a result of the transformation of the field φ mass (dark matter) to energy. In addition, we provide that Ω_{m}≈0,050, Ω_{DM}≈0,2, Ω_{DE}≈0,746, is in excellent agreement with observation data. We explore a generalized formalism of braneworld modified gravity. We also construct a new field equations, which generalize the Einstein field equations. We provide a relation between the extra dimension in 3-brane with the vacuum energy density. We show that the energy density of matter depends directly on the number of dimensions. We manage to find the value of the Gauss-Bonnet coupling α=1/4 which is a good agreement with the results in the literature, this correspondence creates a passage between f(R) gravity and Gauss-Bonnet gravity, this comparison leads to a number of bulk dimensions equal to D=10¹²¹+4.

In this paper any superalgebra is generalized to a new form, namely ultra algebra. We study some algebraic structure results for ultra algebras and we have defined some maps on ultra algebras to know ultra derivation and Jordan ultra derivation. Moreover on certain assumptions we have proved that Jordan ultra derivation is an ultra derivation.

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups $F_4$ and $E_6$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ and $E_6$ symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

The formulation used by the most of studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of the torus, application of those formulations has encountered great difficulty. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of the torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency.

The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

Antimicrobial resistance (AMR) poses a global public health threat, with rates directly linked with consumption. The World Health Organization (WHO) AWaRе-classification aims to guide antibiotic use, which is influenced by drug availability, affordability, and economic policies. In Jordan, a high proportion of consumed antibiotics belong to the 'Watch' category. Data from the WHO-AWaRе classification, the Essential Medicines List, and the Jordan Food and Drug Administration were analyzed. Antibiotics for adults were classified and their cost per Defined Daily Dose (DDD) was determined, then affordability was assessed. In 2023, 43 injectable and 43 oral antibiotics for adults were registered in Jordan. 'Watch' antibiotics were the most common. 'Access' antibiotics had the lowest cost/DDD. 'Rеsеrvе' antibiotics were the most expensive with few generics. Injectable antibiotics had a negative correlation between cost and the number of alternatives. Affordability was higher for oral antibiotics compared to injectable ones. 'Rеsеrvе' antibiotics were generally unaffordable. This study highlights the need to promote 'Access' antibiotics over other categories by encouraging registration of missing ‘Access’ antibiotics and adjusting 'Watch' and 'Rеsеrvе' antibiotic prices. Competition among generics can lead to lower prices, increasing affordability and accessibility. We emphasize the importance of the AWaRе-classification in guiding antibiotic use in Jordan.

Interior designers play a pivotal role in shaping the built environment and catalyzing positive change through the adoption of sustainable design practices. This study centers on the analysis of prevailing attitudes held by interior designers in Jordan towards sustainable interior design practices. Through a comprehensive methodology involving a literature review and a three-part questionnaire, the research explores the benefits, challenges, and integration of sustainability principles. The study highlights substantial awareness (85%) of sustainable interior design's environmental impact and resource preservation. Additionally, 81% acknowledge its enduring significance, and 89% recognize its diverse benefits. While 61% exhibit familiarity, 27% claim professional experience. Among sustainability indicators, energy efficiency scores 4.25, resource efficiency 4.27, and "Design aligns with laws and regulations by the Ministry of Labor" ranks highest at 4.37. This study significantly augments our understanding of sustainable interior design by introducing a comprehensive evaluation framework that encompasses the three sustainability dimensions. It equips decision-makers with a robust tool to identify specific practices that bolster sustainability performance, further advancing the field.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

Phylogeny construction can help to reveal evolutionary relatedness among molecular sequences. The spike (S) gene of SARS-CoV-2 is the subject of an immune selective pressure which increases the variability in such region. This study aimed to identify mutations in the S gene among SARS-CoV-2 sequences collected in the Middle East and North Africa (MENA), focusing on the D614G mutation, that has a presumed fitness advantage. Another aim was to analyze the S gene sequences phylogenetically. The SARS-CoV-2 S gene sequences collected in the MENA were retrieved from the GISAID public database, together with its metadata. Mutation analysis was conducted in Molecular Evolutionary Genetics Analysis software. Phylogenetic analysis was done using maximum likelihood (ML) and Bayesian methods. A total of 553 MENA sequences were analyzed and the most frequent S gene mutations included: D614G=435, Q677H=8, and V6F=5. A significant increase in the proportion of D614G was noticed from (63.0%) in February 2020, to (98.5%) in June 2020 (p<0.001). Two large phylogenetic clusters were identified via ML analysis, which showed an evidence of inter-country mixing of sequences, which dated back to February 8, 2020 and March 15, 2020 (median estimates). The mean evolutionary rate for SARS-CoV-2 was about 6.5 × 10^-3 substitutions/site/year based on large clusters’ Bayesian analyses. The D614G mutation appeared to be taking over the COVID-19 infections in the MENA. Bayesian analysis suggested that SARS-CoV-2 might have been circulating in MENA earlier than previously reported.

For massive multiple-input multiple-output (MIMO) communications, the minimum mean square error (MMSE) scheme provides close to optimal recognition but involves inverting the high-dimensional matrix. A Gauss-Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing is introduced to address this problem. Firstly, the signal is initialized with the best of the three initialization regimes for faster algorithm convergence. Secondly, the signal is processed together with CJ. Finally, the pre-processed result is transferred to the GS detector. The simulation results indicate that the proposed iterative algorithm has a lower BER performance than the GS and improved iterative scheme based on GS in channels with different correlation levels.

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

In the field of business environments, the integration of novel artificial intelligence (AI) techniques has been identified in the literature and theoretical discourse as an essential catalyst for enhancing the decision-making processes. In the contemporary landscape of digital transformation, the application of these techniques becomes essential, despite encountering various hurdles that impede their seamless integration into the rational decision-making process within e-government, which constitutes a critical component of digital government initiatives. This study explores whether similar advancements can be observed within the e-government sector and investigates the impact of using machine learning (ML) as a technique of artificial intelligence on rational decision-making (RDM). Employing an empirical research approach, the study utilized a quantitative methodology, relying on an electronically structured questionnaire survey administered to 163 employees in the e-government sector in Jordan through purposive random sampling. Data analysis was conducted using the SPSS v25 program, complemented by a media-tion analysis using AMOS v23 software. The research findings revealed a significant contribution of using machine learning to enhance rational decision-making and trust levels, with trust positively impacting RDM. Trust was identified as a beneficial mediator in the relationship between machine learning and rational decision-making. Despite certain limitations, this study's outcomes offer substantial insights for researchers and government policy-makers alike, contributing to the advancement of sustainable practices in the e-government domain.

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a ground state. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan-Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has non-zero divergence when phonons or shear stress are present. A possible system where the present kind of monopoles could be observed is BiCu$_2$PO$_6$.

This research focuses on exploring gravitational lensing of the wormhole in Einstein-bumblebee gravity with an antisymmetric tensor. The Gibbons and Werner technique based on the Gauss-Bonnet theorem is utilized to calculate the bending angle of light. The effects of non-plasma and plasma medium on the bending angles are investigated. Furthermore, we examine the deflection angle $\Tilde{\alpha}$ in relation to the impact parameter $\sigma$ and minimal radius $r_{0}$ in both non-plasma and plasma mediums. Our findings indicate that the deflection angle is positively correlated with $r_{0}$, meaning that larger values of $r_{0}$ result in larger deflection angles and smaller values of $r_{0}$ result in smaller deflection angles. On the other hand, the deflection angle $\Tilde{\alpha}$ is inversely related to the impact parameter $\sigma$.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikove-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.

In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in Minkowski 4-space ${\mathbb{E}}_1^4$ . We compute the Gaussian and the mean curvature of the hypersurface. Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal.

The Jordanian Law of Commercial Agents and Intermediaries No. 28 of 2001 and the Emirati Commercial Agency Law No. 2 of 2010 cover all forms of sale contracts through intermediaries. These Laws provide express restrictions and protective provisions on the conduct by local agents of internal commercial agency activities. However, these statutory protections are granted only to registered agencies conducted by national agents.The Jordanian legislator does not regulate the issue of agency exclusivity, which can constitute a restraint of trade and leads to a state of market monopolization. Courts in Jordan have exclusive jurisdiction in settling disputes arising out of agency agreements. However, this exclusive jurisdiction does not cover unregistered commercial agencies which are treated as enforceable commercial contracts under the general provisions prescribed in the Commercial Code.Under the Jordanian Law the principal cannot terminate the agency agreement at any time, but he can dismiss its renewal upon the expiry of its date without justified grounds. Certain statutory protections provided by the Jordanian laws raise barriers to entry to their national markets. This statutory policy violates the specific commitments made by Jordan with respect to market access and national treatment established by the GATS.

We consider several unification problems in mathematics. We refer to transcendental numbers. Also, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

Assessment of the environmental impact of organic chemicals has become an important subject in chemical science. Efficient quantitative descriptors of their impact are their partition coefficients logPow, logKoa and logKaw. We present a group-additivity method that has proven its versatility for the reliable prediction of many other molecular descriptors for the calculation of the first two partition coefficients and indirectly of the third with high dependability. Based on the experimental logPow data of 3332 molecules and the experimental logKoa data of 1900 molecules at 298.15K the respective partition coefficients have been calculated with cross-validated standard deviations of only 0.42 and 0.48 log units and a goodness of fit Q^2 of 0.9599 and 0.9717, respectively, in a range of ca. 17 log units for both descriptors. The third partition coefficient logKaw has been derived from the calculated values of the former two descriptors and compared with the experimentally determined logKaw values of 1937 molecules, yielding a standard deviation of 0.67 log units and a correlation coefficient R^2 of 0.9467. This approach enabled the quick calculation of 29462 logPow, 27069 logKoa and 26220 logKaw values for the more than 37100 molecules of ChemBrain's database available to the public.

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

In this paper, first we use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.

In this paper, we discuss the weak gravitational lensing in the context of stringy black holes. Initially, we examine the deflection angle of photon by charged stringy black hole. For this desire, we compute the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically balanced spacetime of stringy black hole. We also analyze the influence of plasma medium in the weak gravitational lensing for stringy black hole. Moreover, the graphical impact of coupling constant $\alpha$, impact parameter $b$ , black hole charge $Q$ on deflection angle by charged stringy black hole has been studied in plasma as well as non-plasma medium.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

Different drought indices are used to quantify its characteristics. This research applied many approaches to assessing the uncertain SPI and SPEI and the most capturing index of drought. Machine learning algorithms are used to predict drought; TBATS and ARIMA models run diverse input sources including observations, CSIC, and CMIP6-ssp126 datasets. The longest drought duration was 14 months. Drought severity and average intensity were found -24.64 and -1.76, -23.80 and -1.83, -23.57 and -1.96, -23.44 and -2.0 where the corresponding drought categories were SPI 12 -Sweileh, SPI 9 Sweileh, SPI 12 Wadi Dhullail, SPI 12 Amman-Airport. The dominant drought incident occurred between Oct 2020 and Dec 2021. CMIP6 can capture the drought occurrence and severity by measuring SPI but did not capture the severity magnitude same as from observations (-2.87 by observation and -1.77 by CMIP6). Using observed SPI and historical CMIP6, ARIMA was the most accurate than TBATS. Regarding SPEI forecast, ARIMA was the most accurate model to forecast drought index using the observed historical SPEI and CSIC over all stations. The performance metrics ME, RMSE, MAE, and MASE implied significantly promising forecasting models; -0.0046, 0.278, 0.179, &amp; 0.193 respectively for ARIMA and -0.0181, 0.538, 0.416, &amp; 0.466 respectively for TBATS. Hybrid modelling is suggested for more consistency and robustness of forecasting approaches.

In a continuation and extension of an earlier publication, the calculation of the refractivity and polarizability of organic molecules at standard conditions is presented, applying a commonly applicable computer algorithm based on an atom-group additivity method, where the molecules are broken down into their constituting atoms, these again being further characterized by their immediate neighbor atoms. The calculation of their group contributions, carried out by means of a fast Gauss–Seidel fitting calculus, used the experimental data of 5988 molecules from literature. An immediate subsequent ten-fold cross-validation test confirmed the extraordinary accuracy of the prediction of the molar refractivity, indicated by a correlation coefficient R^2 and a cross-validated analog Q^2 of 0.9997, a standard deviation σ of 0.38, a cross-validated analog S of 0.41, and a mean absolute deviation of 0.76%. The high reliability of the predictions has been exemplified with three classes of molecules: ionic liquids, silicon- and boron-containing compounds. The corresponding molecular polarizabilities have been calculated indirectly from the refractivity using the inverse Lorentz-Lorenz relation. In addition, it could be shown that there is a close relationship between the "true" volume and the refractivity of a molecule, revealing an excellent correlation coefficient R^2 of 0.9645 and a mean absolute deviation of 7.53%.

In this article, we calculate the deflection angle of tidal charged black hole (TCBH) in weak field limits. First we obtain the Gaussian optical curvature and then apply the Gauss-Bonnet theorem on it. With the help of Gibbons-Werner method, we are able to calculate the light's deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light's deflection angle in the presence of plasma medium and also check the graphical behavior in the presence of plasma medium. Moreover, we investigate the shadow of TCBH.For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH's shadow in the plasma medium. Hence, we discuss the shadow of the TCBH using the $M87^{*}$ parameters announced by the Event Horizon Telescope.

The catenary shells of revolution are widely used in constructions due to their unique mechanics' feature. However, no publications on this type of shells can be found in the literature. To have a better understanding of the deformation and stress of the catenary shells of revolution, we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations. Numerical simulations are carried out based on both Reissner-Meissner mixed formulations and displacement formulations. Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter $c$, and reveal that the mechanics of the catenary shells of revolution does much better than the spherical shells. Two complete codes in Maple are provided.

In this paper, by considering Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field, we derive exactly a black hole spacetime metric. To test the effect of global monopole field and bumblebee field, which causes the spontaneous Lorentz symmetry breaking, we calculate the weak deflection angle using the Gauss-Bonnet theorem.

In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss–Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effect of the ECKS parameter on the shadow of the black hole and weak deflection angle. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing.

In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter source and anisotropic pressure are influenced by Bohmian quantum effects and calculate its quantum corrected deflection angle. Then, we calculate the deflection angle by naked singularities and compare with the result of wormhole's. Such a novel lensing feature might serve as a way to detect wormholes, naked singularities and also the evidence of Brane-Dicke theory.

The exceptional Jordan algebra is the algebra of $3 \times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan’s algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new U(1) gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

: The silicon single crystals for semiconductor application is usually grown by Czochralski (CZ) method. This paper researches 300mm silicon Czochralski (CZ) crystal growth with CUSP magnetic field for IGBTs substrate application. The different positions of Zero-Gauss plane (ZGP) under CUSP magnetic field are simulated and compared to numerical analysis, investigated melt convection, melt flow velocity near to quartz crucible wall, diffusion boundary layer and effect of initial oxygen concentration in the silicon crystal, and the shape of solid/liquid interface was discussed. The results show that the change of the ZGP of the CMF mainly affects the convection in the melt, which leads to the difference of the thickness of the boundary layer near to the wall of the quartz crucible, and was found to be the key to reduce the oxygen dissolution from the crucible wall and oxygen diffuse into the crystal, along with the differences in the shape of the crystal-melt interface. In addition, we have carried out actual industrial single crystal production under the three configurations. The results show that the experimental data of oxygen content and shape of the crystal-melt interfaces in silicon crystal are consistent with the numerical results.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

In this paper, we study the weak deflection angle using Gauss-Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner's approach, first we acquire the Gaussian optical curvature to use in Gauss-Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we look into the graphical behaviour of bending angles and greybody bounds at some specific values of multiple parameters as well as black holes charges. It is to be mention here that all the results for the electric and magnetic charged black holes solutions reduce into the Schwarzschild black hole solution in the absence of the black holes charges.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

The purpose of this paper is to explore the effect of corporate social responsibility (CSR) on brand image in the apparel industry in Jordan, using the moderating variable of customer consciousness. The current research uses a quantitative, descriptive, cause-effect, and cross-sectional approach, and also it uses a convenience sampling method. Data was collected from 440 respondents. Results indicate that Jordanian Apparel organizations have medium to highly implementing of all items and constructs of CSR, brand image items, and consciousness items. Moreover, there is a strong relationship between CSR dimensions, a medium relationship be-tween each CSR dimension and brand image, a medium relationship between each CSR dimension and consciousness, a medium relationship between total CSR and brand image, a medium relationship between total CSR and consciousness, and the medium relationship between brand image and consciousness. Results of the first model show that total CSR affects the brand image. Where social responsibility has the highest positive effect, followed by ethical responsibility, then economic responsibility, however, environmental responsibility negatively affects the brand image. The second model shows consciousness moderates the effect of CSR on the brand image. The study recommends longitudinal research on the Jordanian Apparel industry, especially to test the effect of environmental responsibility on the brand image. Moreover, the re-search uses customers’ consciousness as a moderating variable, which improves the effect of CSR on brand image. The Apparel industry organizations in Jordan should revise their daily practices particularly environmental responsibility and/or increase their customers’ awareness of their practices. Finally, the current research contributes to existing studies by using consciousness as a moderating variable.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

In this work, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss-Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss-Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of NLED, plasma, and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this paper, we examine the weak deflection angle and greybody factor of magnetized regular black hole. We implement the Gauss-Bonnet theorem on magnetized regular black hole to get the deflection angle. Moreover, we analyze the influence of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. We observe the graphical behaviour of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. Lastly, we study the rigorous bound phenomenon of the greybody factor of magnetized regular black hole. For this purpose we calculate greybody factor results and analyze the graphical behaviour of greybody bound for the different values of the parameters.

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle.

In this paper, we calculate the deflection angle of photon by Casimir wormhole in the weak field limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on the Gaussian optical metric. Then we find the deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. Second, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

Maxwell's fish eye has been known to be a perfect lens in optics. In this letter, using the Gibbons-Werner method, namely Gauss-Bonnet theorem on optical geometry of black hole, we extend the calculation of the weak gravitational lensing within the Maxwell's fisheye as a perfect lensing in medium composed of an isotropic refractive index that near-field information can be obtained from far-field distances. Moreover, these results provide an excellent tool to observe compact massive object by weak gravitational lensing within the dark matter medium and to understand the nature of the dark matter that may effect the gravitational waves. Moreover, we show that Gauss-Bonnet theorem is a global effect and this method can be used as a new tool on any optical geometry of compact objects in dark matter medium.

Nonlinear electrodynamics is known as the generalizations of Maxwell electrodynamics at strong fields and presents interesting features such as curing the classical divergences present in the linear theory when coupled to general relativity. In this paper, we consider the asymptotically flat Reissner-Nordstr\"om black hole solution with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic charge parameters on the black hole, viz. weak deflection angle of photons and massive particles using Gauss-bonnet theorem. Moreover, we apply the Keeton-Petters formalism to confirm our results of the weak deflection angle. Apart from vacuum, their influence in the presence of different media such as plasma and dark matter are probed as well. Finally, We examine the black hole shadow cast using the null-geodesics method and investigate its spherically in-falling thin accretion disk. Our inferences show how the magnetic charge parameter $p$ affects the other physical quantities; so, we impose some constraints on this parameter using the observations from the Event Horizon Telescope.

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and applying the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma as well as non-plasma medium.

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field.

In this article, we analyze the weak gravitational lensing in the context of Einstein-non-linear Maxwell-Yukawa black hole. To this desire, we derive the deflection angle of light by Einstein-non-linear Maxwell-Yukawa black hole using the Gibbons and Werner method. For this purpose, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle of Einstein-non-linear Maxwell-Yukawa black hole. Moreover, we derive the deflection angle of light in the presence of plasma medium. We also analyze the graphical behavior of deflection angle by Einstein-non-linear Maxwell-Yukawa black hole in the presence of plasma as well as non-plasma medium.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

In this paper, we argue that one can calculate the weak deflection angle in the background of Einstein-Maxwell-Dilaton-Axion black hole using the Gauss-Bonnet theorem. To support this, the optical geometry of the black hole with the Gibbons-Werner method are used to obtain the deflection angle of light in the weak field limits. Moreover, we investigate the effect of a plasma medium on deflection of light for a given black hole. Because of dilaton and axion are one of the candidate of the dark matter, it can give us a hint on observation of dark matter which is supported the black hole. Hence we demonstrate the observational viability via showing the effect of the dark matter on the weak deflection angle.

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.

This article introduces a new MfEIT UDESC Mark I system, which consists of a 32-electrode setup featuring a modified Howland current source, low cost, portable and non radiation. The system is capable of reconstruction of electrical conductivity tomographic images at a rate of 30.624 frames per second and about 5 minutes for imaging. The current source employs 0.5 mA, adjacent current application pattern with frequencies ranging from 10 kHz to 1 MHz. The article outlines the hardware, firmware, and software design specifications, which include the design of the current source, calibration procedures, and image reconstruction process. Tomographic images of conductivity were reconstructed in ex vivo healthy pig lungs and those with pneumonia, as a proof of concept for future applications in live pigs. The high spectral power density, combined with real-time system calibration provides clinical advantages in veterinary medicine. The goal is to identify lung areas affected by Mycoplasma hyopneumoniae in pigs, through the analysis of electrical conductivity difference, offering a valuable tool to assist veterinarians for to obtain images of respiratory diseases. The reconstruction method (GREIT) was evaluated with experimental data and It was compared with the Gauss-Newton and Total Variation methods, where GREIT proved to be superior.

In this work, we examine the deflection angle of black hole in effective loop quantum gravity in non-plasma medium via the geometrical technique of Gibbons and Werner in weak field limits. For this, we attain the optical metric and calculate the Gaussian optical curvature and then we apply the Gauss-Bonnet theorem. We also study the influence of the plasma and dark matter mediums on the deflection angle. Further, we obtain the deflection angle by using Keeton and Petters method. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the bending angle and bounds on the greybody factor. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduces to the Schwarzschild black hole solutions when dimensionless non-negative parameter $A_{\lambda}=0$.

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

In this work, we study the weak gravitational lensing in the background of Kerr-Newman black hole with quintessential dark energy. Initially, we compute the deflection angle of light by charged black hole with quintessential dark energy by utilizing the Gauss-Bonnet theorem. Firstly, we suppose the light rays on the equatorial plane in the axisymmetric spacetime. In doing so, we first find the corresponding optical metrics and then calculate the Gaussian optical curvature to utilize in Gauss-Bonnet theorem. Consequently, we calculate the deflection angle of light for rotating charged black hole with quintessence. Additionally, we also find the deflection angle of light for Kerr-Newman black hole with quintessential dark energy. In order to verify our results, we derive deflection angle by using null geodesic equations which reduces to the deflection angle of Kerr solution with the reduction of specific parameters. Furthermore, we analyze the graphical behavior of deflection angle $\Theta$ w.r.t to quintessence parameter $\alpha$, impact parameter $b$, BH charge $Q$ and rotation parameter $a$. Our graphical analysis retrieve various results regarding to the deflection angle by the Kerr-Newman black hole with quintessential dark energy.

We explore the deflection angle in the framework of improved Schwarzschild Black hole utilizing the most advance geometrical path adopted by Gibbon-Werner. To investigate deflection angle of the photon ray by weak gravitational lensing for this black hole, we derive the optical curvature and perform the application of Gauss-Bonnet theorem on the optical metric. Moreover, we study the impacts of the plasma medium in context of the weak gravitational lensing in relate to this black hole. Further, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Also, we find the rigorous bound base upon the greybody factor for improved Schwarzschild black hole. A while later, we contrast our conclusions about deflection angle with the deflection angles of Schwarzschild black hole within plasma and non-plasma mediums.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

This paper is devoted to compute the weak deflection angle for Kalb-Ramond traversable wormhole solution in plasma and dark matter mediums by using the method of Gibbons and Werner. To acquire our results, we evaluate Gaussian optical curvature by utilizing the Gauss-Bonnet theorem in the weak field limits. We also investigate the graphical influence of deflection angle $\tilde{\alpha}$ with respect to the impact parameter $\sigma$ and minimal radius $r_0$ in plasma medium. Moreover, we derive the deflection angle by using different method known as Keeton and Petters method. We also examine that if we remove the effects of plasma and dark matter, the results become identical to that of non-plasma case.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

We discuss a possible scale of gravitational origin at around 10 MeV, or 10⁻¹² cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago.~A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10⁻¹² cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of ~10¹²⁰ multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1–2 MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.