Search results for: Daphne Sobolev

Authors: Daphne Sobolev, Niklas Voege

Abstract:

During the last three decades, consumer ethics perceptions have attracted the attention of a large number of researchers. Nevertheless, little is known about the effect of the cognitive and situational contexts of the decision on ethics judgments. In this paper, the interrelationship between consumers’ ethics perceptions, legality evaluations and mind-sets are explored. Legality evaluations represent the cognitive context of the ethical judgments, whereas mind-sets represent their situational context. Drawing on moral development theories and priming theories, it is hypothesized that both factors are significantly related to consumer ethics perceptions. To test this hypothesis, 289 participants were allocated to three mind-set experimental conditions and a control group. Participants in the mind-set conditions were primed for aggressiveness, politeness or awareness to the negative legal consequences of breaking the law. Mind-sets were induced using a sentence-unscrambling task, in which target words were included. Ethics and legality judgments were assessed using consumer ethics and internet ethics questionnaires. All participants were asked to rate the ethicality and legality of consumer actions described in the questionnaires. The results showed that consumer ethics and legality perceptions were significantly correlated. Moreover, including legality evaluations as a variable in ethics judgment models increased the predictive power of the models. In addition, inducing aggressiveness in participants reduced their sensitivity to ethical issues; priming awareness to negative legal consequences increased their sensitivity to ethics when uncertainty about the legality of the judged scenario was high. Furthermore, the correlation between ethics and legality judgments was significant overall mind-set conditions. However, the results revealed conflicts between ethics and legality perceptions: consumers considered 10%-14% of the presented behaviors unethical and legal, or ethical and illegal. In 10-23% of the questions, participants indicated that they did not know whether the described action was legal or not. In addition, an asymmetry between the effects of aggressiveness and politeness priming was found. The results show that the legality judgments and mind-sets interact with consumer ethics perceptions. Thus, they portray consumer ethical judgments as dynamical processes which are inseparable from other cognitive processes and situational variables. They highlight that legal and ethical education, as well as adequate situational cues at the service place, could have a positive effect on consumer ethics perceptions. Theoretical contribution is discussed.

Keywords: consumer ethics, legality judgments, mind-set, priming, aggressiveness

Procedia PDF Downloads 263

Authors: Lukas Vierus, Thomas Schuster

Abstract:

A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

Procedia PDF Downloads 9

Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

Procedia PDF Downloads 275

Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

Abstract:

The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

Procedia PDF Downloads 204

Authors: Daphne Ashley Sze, Kenneth Santos, Ariane Gabrielle Lim

Abstract:

As women are now given more freedom and choice to pursue employment, the world’s over-all fertility has been decreasing mainly due to the shift in time allocation between working and child rearing. As such, we study the case of the Philippines, where there exists a decreasing fertility rate and increasing openness for women labor participation. We focused on the distinction between fertility and fecundity, the former being the manifestation of the latter and aim to trace and compare the effects of both fecundity and fertility to women’s employment status through the estimation of the reproduction function and multinomial logistic function. Findings suggest that the perception of women regarding employment opportunities in the Philippines links the negative relationship observed between fertility, fecundity and women’s employment status. Today, there has been a convergence in the traditional family roles of men and women, as both genders now have identical employment opportunities that continue to shape their preferences.

Keywords: multinomial logistic function, tobit, fertility, women employment status, fecundity

Procedia PDF Downloads 566

Authors: Ariane C. Lim, Daphne Ashley L. Sze, Kenneth S. Santos

Abstract:

As women are now given more freedom and choice to pursue employment, the world’s over-all fertility has been decreasing mainly due to the shift in time allocation between working and child-rearing. As such, we study the case of the Philippines, where there exists a decreasing fertility rate and increasing openness for women labor participation. We focused on the distinction between fertility and fecundity, the former being the manifestation of the latter and aim to trace and compare the effects of both fecundity and fertility to women’s employment status through the estimation of the reproduction function and multinomial logistic function. Findings suggest that the perception of women regarding employment opportunities in the Philippines links the negative relationship observed between fertility, fecundity and women’s employment status. Today, there has been a convergence in the traditional family roles of men and women, as both genders now have identical employment opportunities that continue to shape their preferences.

Keywords: multinomial logistic function, tobit, fertility, women employment status, fecundity

Procedia PDF Downloads 590

Authors: Daphne Dean C. Arenos, Glorificacion L. Quinopez

Abstract:

This study has been conducted to describe the digitized stories authored by a Grade 1 pupil struggling in reading. The main goal was to find out the effect of authoring digital stories on the reading skill of a grade 1 pupil in terms of vocabulary and sequencing skills. To be able to explicate the data collected, a case study approach has been chosen. This case study focused on a 6 years old Filipino child born and raised in Spain and has just transferred to a private school a year ago. The pupil’s struggles in reading, as well as her experiences with digitized stories, were further described. The findings revealed that authoring digital stories facilitate the reading progress of a struggling pupil. The presence of literary elements in the pupil’s stories built her vocabulary and sequencing skills. Hence, authoring digital stories serve as an appropriate and effective scaffold for struggling readers.

Keywords: literary elements, reading skill, scaffold, sequencing skill, vocabulary

Procedia PDF Downloads 103

Authors: Nicolae Pascu

Abstract:

Aside from being a fundamental tool in Complex analysis, Schwarz Lemma-which was finalized in its most complete form at the beginning of the last century-generated an important area of research in various fields of mathematics, which continues to advance even today. We present some properties of analytic functions in the half-plane which satisfy the conditions of the classical Schwarz Lemma (Carathéodory functions) and obtain a generalization of the well-known Aleksandrov-Sobolev Lemma for analytic functions in the half-plane (the correspondent of Schwarz-Pick Lemma from the unit disk). Using this Schwarz-type lemma, we obtain a characterization for the entire class of Carathéodory functions, which might be of independent interest. We prove two monotonicity properties for Carathéodory functions that do not depend upon their normalization at infinity (the hydrodynamic normalization). The method is based on conformal mapping arguments for analytic functions in the half-plane satisfying appropriate conditions, in the spirit of Schwarz lemma. According to the research findings in this paper, our main results give estimates for the modulus and the argument for the entire class of Carathéodory functions. As applications, we give several extensions of Julia-Wolf-Carathéodory Lemma in a half-strip and show that our results are sharp.

Keywords: schwarz lemma, Julia-wolf-caratéodory lemma, analytic function, normalization condition, caratéodory function

Procedia PDF Downloads 156

Authors: Daphne Alroy-Thiberge

Abstract:

Trauma-impacted individuals present unique treatment challenges that include high reactivity, hyper-and hypo-arousal, poor adherence to therapy, as well as powerful transference and counter-transference experiences in therapy. This work provides an overview of the clinical tenets most often encountered in trauma-impacted individuals. Further, it provides readily applicable clinical techniques to optimize therapeutic rapport and facilitate accelerated positive mental health outcomes. Finally, integrated neuroscience and clinical evidence-based data are discussed to shed new light on crisis states in trauma-impacted individuals. This knowledge is utilized to provide effective and concrete interventions towards rapid and successful de-escalation of the impacted individual. A highly interactive, adult-learning-principles-based modality is utilized to provide an organic learning experience for participants. The information and techniques learned aim to increase clinical effectiveness, reduce staff injuries and burnout, and significantly enhance positive mental health outcomes and self-determination for the trauma-impacted individuals treated.

Keywords: clinical competencies, crisis interventions, psychotherapy techniques, trauma informed care

Procedia PDF Downloads 60

Authors: D. Kabeya Nahum, L. Y. Kabeya Mukeba

Abstract:

In this work, the design of surface defects some support of the anchor rod ball joint. The future adhesion contact was rocking in manufacture machining, for giving by the numerical analysis of a short simple solution of thermo-mechanical coupled problem in process engineering. The analysis of geometrical evaluation and the quasi-static and dynamic states are discussed in kinematic dimensional tolerances onto surfaces of part. Geometric modeling using the finite element method (FEM) in rough part of such phase provides an opportunity to solve the nonlinearity behavior observed by empirical data to improve the discrete functional surfaces. The open question here is to obtain spherical geometry of drain wear with the operation of rolling. The formulation with (1 ± 0.01) mm thickness near the drain wear semi-finishing tool for studying different angles, do not help the professional factor in design cutting metal related vibration, friction and interface solid-solid of part and tool during this physical complex process, with multi-parameters no-defined in Sobolev Spaces. The stochastic approach of cracking, wear and fretting due to the cutting forces face boundary layers small dimensions thickness of the workpiece and the tool in the machining position is predicted neighbor to ‘Yakam Matrix’.

Keywords: FEM, geometry, part, simulation, spherical surface engineering, tool, workpiece

Procedia PDF Downloads 244

Authors: Eduard Marusic-Paloka

Abstract:

The Darcy-Weisbach formula is used to compute the pressure drop of the fluid in the pipe, due to the friction against the wall. Because of its simplicity, the Darcy-Weisbach formula became widely accepted by engineers and is used for laminar as well as the turbulent flows through pipes, once the method to compute the mysterious friction coefficient was derived. Particularly in the second half of the 20th century. Formula is empiric, and our goal is to derive it from the basic conservation law, via rigorous asymptotic analysis. We consider the case of the laminar flow but with significant Reynolds number. In case of the perfectly smooth pipe, the situation is trivial, as the Navier-Stokes system can be solved explicitly via the Poiseuille formula leading to the friction coefficient in the form 64/Re. For the rough pipe, the situation is more complicated and some effects of the roughness appear in the friction coefficient. We start from the Navier-Stokes system in the pipe with periodically corrugated wall and derive an asymptotic expansion for the pressure and for the velocity. We use the homogenization techniques and the boundary layer analysis. The approximation derived by formal analysis is then justified by rigorous error estimate in the norm of the appropriate Sobolev space, using the energy formulation and classical a priori estimates for the Navier-Stokes system. Our method leads to the formula for the friction coefficient. The formula involves resolution of the appropriate boundary layer problems, namely the boundary value problems for the Stokes system in an infinite band, that needs to be done numerically. However, theoretical analysis characterising their nature can be done without solving them.

Keywords: Darcy-Weisbach law, pipe flow, rough boundary, Navier law

Procedia PDF Downloads 316

Authors: Daphne Fietz

Abstract:

This paper builds on a reflection on an autobiographical experience of uncanniness during fieldwork in the white Afrikaner settlement Orania in South Africa. Drawing on Kristeva’s theory of abjection to establish a theory of Whiteness which is based on boundary threats, it is argued that the uncanny experience as the emergence of the abject points to a moment of crisis of the author’s Whiteness. The emanating abject directs the author to her closeness or convergence with Orania's inhabitants, that is a reciprocity based on mutual Whiteness. The experienced confluence appeals to the author’s White complicity to racism. With recourse to Butler’s theory of subjectivation, the abject, White complicity, inhabits both the outside of a discourse on racism, and of the 'self', as 'I' establish myself in relation to discourse. In this view, the qualities of the experienced abject are linked to the abject of discourse on racism, or, in other words, its frames of intelligibility. It then becomes clear, that discourse on (overt) racism functions as a necessary counter-image through which White morality is established instead of questioned, because here, by White reasoning, the abject of complicity to racism is successfully repressed, curbed, as completely impossible in the binary construction. Hence, such discourse endangers a preservation of racism in its pre-discursive and structural forms as long as its critique does not encompass its own location and performance in discourse. Discourse on overt racism is indispensable to White ignorance as it covers underlying racism and pre-empts further critique. This understanding directs us towards a form of critique which does necessitate self-reflection, uncertainty, and vigilance, which will be referred to as a discourse of relationality. Such a discourse diverges from the presumption of a detached author as a point of reference, and instead departs from attachment, dependence, mutuality and embraces the visceral as a resource of knowledge of relationality. A discourse of relationality points to another possibility of White engagement with Whiteness and racism and further promotes a conception of responsibility, which allows for and highlights dispossession and relationality in contrast to single agency and guilt.

Keywords: abjection, discourse, relationality, the visceral, whiteness

Procedia PDF Downloads 128

Authors: Lina Wu, Jia Liu, Ye Li

Abstract:

The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

Procedia PDF Downloads 244

Authors: Amina Beldjazia, Djamel Alatou, Khaled Missaoui

Abstract:

The forest of Mahouna is a part of the mountain range of the Tell Atlas in the northeast of Algeria. It is characterized by a significant biodiversity. The management of this resource requires thorough the understanding of the current state of the vegetation (inventories), degradation factors and ongoing monitoring of the various long-term ecological changes. Digital mapping is a very effective way to in-depth knowledge of natural resources. The realization of a vegetation map based on satellite images, aerial photographs and the use of geographic information system (GIS), shows large values results of the vegetation of the massif in the scientific view point (the development of a database of the different formations that exist on the site, ecological conditions) and economic (GIS facilitate our task of managing the various resources and diversity of the forest). The methodology is divided into three stages: the first involves an analysis of climate data (1988 to 2013); the second is to conduct field surveys (soil and phytoecological) during the months of June and July 2013 (10 readings), the third is based on the development of different themes and synthetic cards by software of GIS (ENVI 4.6 and 10 ARCMAP). The results show: cork oak covers an area of 1147 ha. Depending on the environmental conditions, it rests on sandstone and individualizes between 3 layers of vegetation from thermo-mediterranean (the North East part with 40ha), meso-Mediterranean (1061 ha) and finally the supra-Mediterranean (46ha ). The map shows the current actual state of the cork oak forest massif of Mahouna, it is an older forest (>150 years) where regeneration is absent because of several factors (fires, overgrazing, leaching, erosion, etc.). The cork oak is in the form of dense forest with Laburnum and heather as the dominant species. It may also present in open forest dominated by scrub species: Daphne gniduim, Erica arborea, Calycotome spinosa, Phillyrea angustifolia, Lavandula stoechas, Cistus salvifolius.

Keywords: biodiversity, environmental, Mahouna, Cork oak

Procedia PDF Downloads 410

Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

Procedia PDF Downloads 39

Authors: Jitendra Pratap, Daphne Prybyszcuk, Luke Elliott, Arnold Ng

Abstract:

Introduction: Coronary CT angiography is a non-invasive imaging technique for the assessment of coronary artery disease and has high sensitivity and negative predictive value. However, the correlation between the degree of CT coronary stenosis and the significance of hemodynamic obstruction is poor. The assessment of myocardial perfusion has mostly been undertaken by Nuclear Medicine (SPECT), but it is now possible to perform stress myocardial CT perfusion (CTP) scans quickly and effectively using CT scanners with high temporal resolution. Myocardial CTP is in many ways similar to neuro perfusion imaging technique, where radiopaque iodinated contrast is injected intravenously, transits the pulmonary and cardiac structures, and then perfuses through the coronary arteries into the myocardium. On the Siemens Force CT scanner, a myocardial perfusion scan is performed using a dynamic axial acquisition, where the scanner shuffles in and out every 1-3 seconds (heart rate dependent) to be able to cover the heart in the z plane. This is usually performed over 38 seconds. Report: A CT myocardial perfusion scan can be utilised to complement the findings of a CT Coronary Angiogram. Implementing a CT Myocardial Perfusion study as part of a routine CT Coronary Angiogram procedure provides a ‘One Stop Shop’ for diagnosis of coronary artery disease. This case study demonstrates that although the CT Coronary Angiogram was within normal limits, the perfusion scan provided additional, clinically significant information in regards to the haemodynamics within the myocardium of a patient with Hypertrophic Obstructive Cardio Myopathy (HOCM). This negated the need for further diagnostics studies such as cardiac ECHO or Nuclear Medicine Stress tests. Conclusion: CT coronary angiography with adenosine stress myocardial CTP was utilised in this case to specifically exclude coronary artery disease in conjunction with accessing perfusion within the hypertrophic myocardium. Adenosine stress myocardial CTP demonstrated the reduced myocardial blood flow within the hypertrophic myocardium, but the coronary arteries did not show any obstructive disease. A CT coronary angiogram scan protocol that incorporates myocardial perfusion can provide diagnostic information on the haemodynamic significance of any coronary artery stenosis and has the potential to be a “One Stop Shop” for cardiac imaging.

Keywords: CT, cardiac, myocardium, perfusion

Procedia PDF Downloads 86

Authors: Daphne Meza, Louie Abejar, David A. Rubenstein, Wei Yin

Abstract:

Endothelial cell (ECs) morphology and function is highly impacted by the mechanical stresses these cells experience in vivo. Any change in the mechanical environment can trigger pathological EC responses. A detailed understanding of EC morphological response and function upon subjection to individual and simultaneous mechanical stimuli is needed for advancement in mechanobiology and preventive medicine. To investigate this, a programmable device capable of simultaneously applying physiological fluid shear stress (FSS) and cyclic strain (CS) has been developed, characterized and validated. Its validation was performed both experimentally, through tracer tracking, and theoretically, through the use of a computational fluid dynamics model. The effectiveness of the device was evaluated through EC morphology changes under mechanical loading conditions. Changes in cell morphology were evaluated through: cell and nucleus elongation, cell alignment and junctional actin production. The results demonstrated that the combined FSS-CS stimulation induced visible changes in EC morphology. Upon simultaneous fluid shear stress and biaxial tensile strain stimulation, cells were elongated and generally aligned with the flow direction, with stress fibers highlighted along the cell junctions. The concurrent stimulation from shear stress and biaxial cyclic stretch led to a significant increase in cell elongation compared to untreated cells. This, however, was significantly lower than that induced by shear stress alone, indicating that the biaxial tensile strain may counteract the elongating effect of shear stress to maintain the shape of ECs. A similar trend was seen in alignment, where the alignment induced by the concurrent application of shear stress and cyclic stretch fell in between that induced by shear stress and tensile stretch alone, indicating the opposite role shear stress and tensile strain may play in cell alignment. Junctional actin accumulation was increased upon shear stress alone or simultaneously with tensile stretch. Tensile stretch alone did not change junctional actin accumulation, indicating the dominant role of shear stress in damaging EC junctions. These results demonstrate that the shearing-stretching device is capable of applying well characterized dynamic shear stress and tensile strain to cultured ECs. Using this device, EC response to altered mechanical environment in vivo can be characterized in vitro.

Keywords: cyclic stretch, endothelial cells, fluid shear stress, vascular biology

Procedia PDF Downloads 341

Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

Procedia PDF Downloads 53

Authors: Sandhya Rijal, Saroj Adhikari, Ramesh R. Pant

Abstract:

Non-Timber Forest Products (NTFPs) have attracted substantial interest in the recent years with the increasing recognition that these can provide essential community needs for improved and diversified rural livelihood and support the objectives of biodiversity conservation. Nevertheless, various challenges are witnessed in their sustainable harvest and management. Assuming that sustainable management with community stewardship can offer one of the solutions to existing challenges, the study assesses the linkages between NTFPs and rural livelihood in Lamabagar village of Dolakha, Nepal. The major objective was to document the status of NTFPs and their contributions in households of Lamabagar. For status documentation, vegetation sampling was done using systematic random sampling technique. 30 plots of 10 m × 10 m were laid down in six parallel transect lines at horizontal distance of 160 m in two different community forests. A structured questionnaire survey was conducted in 76 households (excluding non-response rate) using stratified random sampling technique for contribution analysis. Likewise, key informant interview and focus group discussions were also conducted for data triangulations. 36 different NTFPs were recorded from the vegetation sample in two community forests of which 50% were used for medicinal purposes. The other uses include fodder, religious value, and edible fruits and vegetables. Species like Juniperus indica, Daphne bholua Aconitum spicatum, and Lyonia ovalifolia were frequently used for trade as a source of income, which was sold in local market. The protected species like Taxus wallichiana and Neopicrorhiza scrophulariiflora were also recorded in the area for which the trade is prohibited. The protection of these species urgently needs community stewardship. More than half of the surveyed households (55%) were depending on NTFPs for their daily uses, other than economic purpose whereas 45% of them sold those products in the market directly or in the form of local handmade products as a source of livelihood. NTFPs were the major source of primary health curing agents especially for the poor and unemployed people in the study area. Hence, the NTFPs contributed to livelihood under three different categories: subsistence, supplement income and emergency support, depending upon the economic status of the households. Although the status of forest improved after handover to the user group, the availability of valuable medicinal herbs like Rhododendron anthopogon, Swertia nervosa, Neopicrorhiza scrophulariiflora, and Aconitum spicatum were declining. Inadequacy of technology, lack of easy transport access, and absence of good market facility were the major limitations for external trade of NTFPs in the study site. It was observed that people were interested towards conservation only if they could get some returns: economic in terms of rural settlements. Thus, the study concludes that NTFPs could contribute rural livelihood and support conservation objectives only if local communities are provided with the easy access of technology, market and capital.

Keywords: contribution, medicinal, subsistence, sustainable harvest

Procedia PDF Downloads 96