Equality Of Means Research Articles

REMARKS ON INEQUALITIES WITH PARAMETER BY CONFORMABLE FRACTIONAL INTEGRALS

We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite–Hadamard-, Simpson-, and Bullen-type inequalities which are proved in earlier published papers. More precisely, some inequalities are acquired by taking advantage of the convexity, the Hölder, and the power mean inequalities. Finally, examples are given to illustrate the investigated results.

Gender equality in family relations: legal aspects of protecting the rights of women and men in marriage

Gender equality in family legal relations is one of the main foundations of modern legal and social development. The article is devoted to the systematic analysis of the principle of gender equality in family relations as one of the fundamental tasks of the state and society. This study acquires special importance in the context of global political processes, international obligations of Ukraine and its European choice. The theoretical and practical importance of this issue is decisive for legal principles and the development of national society. Implementation of the principles of gender equality in family relations is important not only from the point of view of justice, but also for ensuring the harmonious development of society in general. The article examines the concept of gender equality in detail and determines its impact on the realization of property rights of participants in family relationships. On the basis of an in-depth analysis of scientific provisions, the legal nature of economic relations of spouses and their importance in the science of family law have been clarified. It is emphasized that family legislation reflects the concept of gender, taking into account all aspects of gender issues. Its purpose is to strengthen the principles of egalitarian democracy in the family, to ensure equal opportunities for the realization of constitutional rights, freedoms and duties of both an individual and a citizen. Legal awareness is defined as the basis of the mechanism for ensuring gender equality in Ukraine. The importance of gender equality for achieving stability and harmony in the family and society in general is emphasized. It has been established that there are problems of low legal awareness of citizens in general and specific problems of gender inequality in the country. It has been studied that gender equality in family relations is becoming more and more relevant and necessary in modern society. The meaning of gender equality as equal recognition of rights and opportunities for men and women in all aspects of family life is considered. Through the analysis of the legal aspects of the protection of the rights of women and men in marriage, highlighting the practical aspects of the realization of these rights and the analysis of socio-cultural influences, the formation and application of gender equality in modern family relations has been studied. It was noted that achieving gender equality in family relationships is a complex process that includes both legal and socio-cultural aspects. In particular, this issue is closely related to the fight against gender stereotypes, which can still affect attitudes towards the roles of men and women in the family. Therefore, the effective provision of gender equality in family legal relations requires not only the improvement of legislation, but also a change in public consciousness.

Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

UNVEILING GENDER BIAS: AN ANALYSIS THE DECONSTRUCTION OF MEANING IN ADVERTISING THROUGH CRITICAL DISCOURSE ANALYSIS

Society's current views on gender equality have become a crucial topic of in-depth discussion, especially those widely promoted by modern society in advertising. It proves that the meaning of gender equality recognized in society has shifted from its true meaning. This research aims to raise the issue of gender equality by deconstructing the meaning of gender equality in advertising from a feminist perspective using Critical Discourse Analysis. This research uses a descriptive qualitative research design with a critical discourse analysis approach by Fairclough, which focuses on three dimensions: the textual, discursive, and sociocultural practice dimensions. The data collection technique in this research uses the SBLC (Simak Bebas Libat Cakap) and note-taking techniques, in which the researcher listens to the utterances contained in the advertisement and records the utterances that will be used as data objects. Data sources were obtained from advertisements published on YouTube, totaling four advertisements with the theme of gender equality. The results of this study provide a deep understanding of the meaning of gender equality in the media and society. They can build different stereotypes or realities and be well-accepted by society. In addition, the deconstruction of meaning allows us as researchers or academics to look more critically at the discourse in these advertisements and whether gender equality always puts men in a position that dominates women.

Estimations of Karcher mean by Hadamard product

In this paper, we estimate the difference between the Hadamard product and the Karcher mean of n positive invertible operators on the Hilbert space in terms of the Specht ratio and the Kantorovich constant. Also, we improve the obtained inequalities in the case of n=2. Moreover, we give ratio inequalities of the operator power means by the Hadamard product.

Depoliticized and decontextualized equality promotion in the gender equality planning of Finnish comprehensive schools

ABSTRACT This study critically examines gender equality planning (GEP), which has been obligatory in all Finnish comprehensive schools since 2015. GEP has been welcomed as a promising method of systemizing perspectives on gender in Finnish basic education. A regionally representative, discretional sample of gender equality plans (N = 140) was analysed using a critical discourse approach to examine how these plans discursively bent, stretched, fixed or shrank the meaning of gender equality along with the consequences of these approaches for equality promotion. The analysis shows that the GE plans constantly bent and stretched equality to separate it from gender and fixed it to free-floating gender equality measures, which left gendered power relations undisturbed. Consequently, equality promotion was represented as depoliticized. However, through the shrinking, the contextual construction of gendered power relations was recognized, and GEP exhibited the potential to politicize gender equality. In this paper, we argue that GEP has potential in gender equality promotion if the planning processes recognize contextual construction of gendered power relations and if equality promotion is not reduced to technical measures. Otherwise, the tool might actually impede equality rather than promoting it.

On Bernstein and Turán-type integral mean estimates for polar derivative of a polynomial

Let p(z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p(z)$\\end{document} be a polynomial of degree n having no zero in |z|<k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|z|< k$\\end{document}, k≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$k\\leq 1$\\end{document}, then Govil [Proc. Nat. Acad. Sci., 50(1980), 50-52] proved max|z|=1|p′(z)|≤n1+knmax|z|=1|p(z)|,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\max _{|z|=1}|p'(z)|\\leq \\frac{n}{1+k^{n}}\\max _{|z|=1}|p(z)|, $$\\end{document} provided |p′(z)|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|p'(z)|$\\end{document} and |q′(z)|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|q'(z)|$\\end{document} attain their maxima at the same point on the circle |z|=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|z|=1$\\end{document}, where q(z)=znp(1z‾)‾.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q(z)=z^{n}\\overline{p\\bigg(\\frac{1}{\\overline{z}}\\bigg)}. $$\\end{document} In this paper, we present integral mean inequalities of Turán- and Erdös-Lax-type for the polar derivative of a polynomial by involving some coefficients of the polynomial, which refine some previously proved results and one of our results improves the above Govil inequality as a special case. These results incorporate the placement of the zeros and some coefficients of the underlying polynomial. Furthermore, we provide numerical examples and graphical representations to demonstrate the superior precision of our results compared to some previously established results.

Dissecting Gender Bias: Critical Discourse Analysis of Advertisements in Indonesia

This research aims to identify gender equality issues by deconstructing the meaning of gender equality in advertisements from a feminist perspective through Critical Discourse Analysis. This research uses a descriptive qualitative research design with a Critical Discourse Analysis approach developed by Fairclough, which focuses on three main dimensions: textual dimension (microstructural), text production practice dimension (mesostructural), and socio-cultural practice dimension (macrostructural). Research data were obtained through interviews with informants as well as from advertisements related to gender equality aired on YouTube. Data collection techniques include interviews and the method of free listening and listening (SBLC) with note-taking techniques. The data collected was then analyzed using triangulation and deconstruction methods to reveal the ideology contained in the ad text and compare it with the informants' views. The results of this study show that societal norms often undermine women's abilities and limit women's roles to the domestic domain or as companions to their husbands. This research is expected to provide a deeper understanding of the meaning of gender equality in advertising media and help build a new perspective that is more inclusive and acceptable to society in Indonesia. The phenomenon of gender equality remains a challenge in many countries, including Pakistan and Nigeria, although the approaches and responses to this inequality differ in each country. In Pakistan, gender representations in media and advertising tend to reinforce traditional stereotypes, while in Nigeria, women are more active in fighting inequality through platforms such as blogs, which are used to criticize patriarchy and fight for social change. Deconstructing meaning in advertising allows researchers and academics to critically evaluate whether gender equality always places men in a dominant position over women, thus opening space for deeper analysis and more equitable solutions.

Optimal power-type Heronian and Lehmer means inequalities for the complete elliptic integrals

In this paper, we prove that the inequalities H p ( K ( r ) , E ( r ) ) < π 2 , L q ( K ( r ) , E ( r ) ) < π 2 hold for all r ∈ ( 0 , 1 ) if and only if p ≤ − log ⁡ 3 / log ⁡ ( π / 2 ) and q<−1, where H p ( a , b ) and L q ( a , b ) are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b, and K ( r ) and E ( r ) are respectively the complete elliptic integrals of the first and second kinds.

Symmetric SAGE and SONC forms, exactness and quantitative gaps

The classes of sums of arithmetic-geometric exponentials (SAGE) and of sums of nonnegative circuit polynomials (SONC) provide nonnegativity certificates which are based on the inequality of the arithmetic and geometric means. We study the cones of symmetric SAGE and SONC forms and their relations to the underlying symmetric nonnegative cone.As main results, we provide several symmetric cases where the SAGE or SONC property coincides with nonnegativity and we present quantitative results on the differences in various situations. The results rely on characterizations of the zeroes and the minimizers for symmetric SAGE and SONC forms, which we develop. Finally, we also study symmetric monomial mean inequalities and apply SONC certificates to establish a generalized version of Muirhead's inequality.

Clinical profiling, treatment characteristics and outcome in Behcet's Disease (BD)-A retrospective cohort study from Karnataka Rheumatology Association (KRA).

Behcet's disease (BD) has a heterogeneous and unpredictable phenotype that differs in various geographical areas. To describe the clinical phenotype & outcome of Behcet's disease(BD) from Karnataka, India and compare them with large cohorts from endemic regions. Databases of practising rheumatologists from Karnataka were reviewed to retrieve clinical characteristics, course of illness, prescribing information and outcome at last follow-up of patients clinically diagnosed as BD. The classification criteria, namely revised International criteria for Behcet's disease (rICBD) and International study group (ISG) criteria were applied. Outcome was defined as complete or partial remission, persistent disease or relapse. We included 72 patients, equal gender distribution and mean age 37.4 ± 12.8years from 8 rheumatology centres. Commonest presentations were recurrent oral aphthosis 58(80.6%), genital ulcers 36(50%) and ocular manifestations 40(55.6%). Three-quarters [51/72(70.8%)] fulfilled rICBD criteria whereas only half [36/72(50%)] fulfilled ISG criteria. Apart from glucocorticoids [53/72(73.6%)], frequently prescribed therapies were colchicine 39(54.2%) and azathioprine 35(48.6%). Eleven-patients received biologics(anti-TNF-α) and JAK inhibitors to treat severe organ involvement. HLA-B*51 and pathergy tests were positive in 27/45(60%) and 12/34(35.3%) patients respectively. Outcomes were documented in 94.4%(68/72) patients at median follow-up of 24 (12;36) months. Majority [46/68(67.6%)] had complete remission, 17/68(25%) had partial remission, 4/68(5.9%) had persistent while 1/68(1.5%) had relapsing course. Majority of BD patients had orogenital aphthosis and ocular manifestations and an excellent response to treatment. Key Points • In our region, Behçet's Disease primarily manifests with recurrent oral aphthae and ocular involvement, with comparatively lower incidence of severe genital ulcers and neurological involvement than in endemic regions. • Apart from glucocorticoids, colchicine and azathioprine are the most commonly used agents. Biologics and JAK inhibitors are prescribed infrequently, primarily in cases of severe organ involvement. • A significant proportion of patients achieved either complete or partial remission during follow-up, with no observed mortality suggesting a milder disease course and better outcome compared to endemic regions. • Gender, HLA-B*51 status, and pathergy response did not exert any significant influence on the clinical profile or outcome in BD patients in Karnataka.

New Results on Simpson-Type Inequalities for Co-ordinated Convex Function by Generalized Conformable Integrals

In this paper, firstly, we prove an identity involving generalized conformable integrals. By using this obtained identity, we establish several Simpson-type inequalities for differentiable co-ordinated convex function by means of generalized conformable fractional integrals. More precisely, some Simpson-type inequalities are obtained using the well-known Hölder and Power mean inequalities. Furthermore, we also consider some special cases which can be deduced from the main results.

Strong F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {F}$\\end{document}-convexity and concavity and refinements of some classical inequalities

The concept of strong F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathcal {F}}$\\end{document}-convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathcal {F}}$\\end{document}-concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.

Integral means of solutions of the one-dimensional Poisson equation with Robin boundary conditions

Consider the one-dimensional Poisson equation −u″=f on the interval [−π,π], where f is an non-negative integrable function, with Robin boundary conditions −u′(−π)+αu(−π)=u′(π)+αu(π)=0, where α>0 is a constant. In this paper we prove inequalities for the convex integral means of solutions of this problem, using the polarization of functions and its properties. We find solutions with maximal convex integral means and prove their uniqueness.

On Some New Dynamic Hilbert-Type Inequalities Across Time Scales

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T=N and T=R), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as T=qN0 for q&gt;1, which, to the best of the authors’ knowledge, is a largely novel conclusion.

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.

On integrals of birth–death processes at random time

In this paper, we consider a time-changed path integral of the homogeneous birth–death process. Here, the time changes according to an inverse stable subordinator. It is shown that its joint distribution with the time-changed birth–death process is governed by a fractional partial differential equation. In a linear case, the explicit expressions for the Laplace transform of their joint generating function, means, variances and covariance are obtained. The limiting behavior of this integral process has been studied. Later, we consider the fractional integrals of linear birth–death processes and their time-changed versions. The mean values of these fractional integrals are obtained and analyzed. In a particular case, it is observed that the time-changed path integral of the linear birth–death process and the fractional integral of time-changed linear birth–death process have equal mean growth.

Forensic Analysis of Sexual Dimorphism from Facial Photographs

Abstract Background: Techniques for identifying facial features and proving the individuality of a person’s facial features are used in forensic anthropology. Aims and Objectives: A common method in this area is cranial anthropometry, which has uses in facial reconstruction, locating unidentified remains, and identifying criminal suspects. Materials and Methods: A study analyzed 200 standard full-face photographs of 50 males and 50 females to compare frontal and lateral facial images and identify male and female facial traits. We located landmarks and measured the distances between them. The data were analyzed using statistical tests like t-tests and analysis of variance (ANOVA) tests. Result: The results showed that in 100% of the suggested measurements for both males and females, there were no statistically significant differences (P &gt; 0.05) between frontal and lateral views. The ANOVA test, however, showed that all suggested measurements showed differences in the lateral aspect, while only 76.92% of them showed differences between the male and female groups in the frontal aspect. Conclusion: In conclusion, statistically significant differences were found, rejecting the null hypothesis of equal means, when the level of significance (α) was lower than the P value (0.05). On the other hand, the null hypothesis was accepted when statistically insignificant differences were found and the level of significance was higher than the P value. Although there were differences between males and females in different views, the distances between landmarks in frontal and lateral views of the same person were generally similar. Measurements taken in the lateral aspect were more accurate and displayed greater sexual dimorphism variation compared to those taken in the frontal aspect.

PANDANGAN AL-QUR'AN TENTANG SOLUSI PENGENTASAN KEMISKINAN KELUARGA DAN MASYARAKAT MUSLIM MELALUI PENDEKATAN TAFSIR TEMATIK

This research aims to reveal the Al-Qur'an's views on solutions to poverty alleviation in Muslim families and communities, by identifying and classifying Al-Qur'an verses that discuss poverty and solutions to its alleviation in the contemporary era. The research method used is a literature study with secondary data sourced from verses of the Al-Qur'an and their interpretations, using a descriptive analytical approach. In the discussion it was revealed that the Qur'an offers several concrete and holistic solutions in overcoming poverty, which includes economic, social and spiritual aspects, including: Implementation of the zakat, infaq and alms and waqf systems as a means of economic equality and philanthropy in Islam, In this way, there will be an integration of spiritual and material aspects in alleviating poverty. The application of Al-Qur'an solutions in alleviating poverty starts from the individual, family, community level, up to the state level as a policy regulator.