Search results for: Arrow’s impossibility theorem

Authors: Hao-Hsi Tseng, Hsin-Yun Lee

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The Most Advantageous Tender (MAT) has been criticized for its susceptibility to dictatorial situations and for its processing of same score, same rank issues. This study applies the four criteria from Arrow's Impossibility Theorem to construct a mechanism for revealing illegitimate scores in scoring methods. While commonly be used to improve on problems resulting from extreme scores, ranking methods hide significant defects, adversely affecting selection fairness. To address these shortcomings, this study relies mainly on the overall evaluated score method, using standardized scores plus normal cumulative distribution function conversion to calculate the evaluation of vender preference. This allows for free score evaluations, which reduces the influence of dictatorial behavior and avoiding same score, same rank issues. Large-scale simulations confirm that this method outperforms currently used methods using the Impossibility Theorem.

Keywords: Arrow’s impossibility theorem, cumulative normal distribution function, most advantageous tender, scoring method

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Authors: Fahad Suleiman, Sammani Abdullahi

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The study depicts that a Wedderburn Artin – theorem for rings is considered to be a semisimple ring R which is isomorphic to a product of finitely many mi by mi matrix rings over division rings Di, for some integers n_i, both of which are uniquely determined up to permutation of the index i. It has been concluded that when R is simple the Wedderburn – Artin theorem is known as Wedderburn’s theorem.

Keywords: Commutativity, Wedderburn theorem, Semisimple ring, R module

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Authors: Ayubi Wirara, Ardya Suryadinata

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Improper application of the RSA algorithm scheme can cause vulnerability to attacks. The attack utilizes the relationship between broadcast messages sent to the user with some fixed polynomial functions that belong to each user. Scheme attacks carried out by applying the Chinese Remainder Theorem to obtain a general polynomial equation with the same modulus. The formation of the general polynomial becomes a first step to get back the original message. Furthermore, to solve these equations can use Coppersmith's theorem.

Keywords: RSA algorithm, broadcast message, Chinese Remainder Theorem, Coppersmith’s theorem

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Authors: A. K. O’Loughlin

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Identity doesn’t exist in discrete categories as it is defined. Kevin Kumashiro reveals the phrase 'an impossibility of identity' in Troubling Education (2000), an investigation of the intersections of culture and gender and the impact of erasure for queer POC identity. This underscores the essentiality of an insider or an outsider identity and the appearance of 'contradiction' or impossibility of these identities. The contradictions between us as subject in our own stories and in the stories of others are often silenced. This silencing of complex, 'contradicting' identity has unmissable implications in the classroom; the developing student in question is done a serious disservice, from which they may never recover. There is no more important point of contact than the teacher, for willingness to encounter a developing person as they are, not as we already think they are, or 'know' them to be, or think they should be. To decide how to regard them based on our own unilateral identity and its associated exhortations and injunctions is, as Hannah Arendt writes in The Origins of Totalitarianism (1951), to sell off our ability to rise, human-like, to the challenge of investigating things as they are. A re-reading of Kumashiro’s impossibility of identity becomes possible through the investigation of pluralism. Identities become possible and un-paradoxical by the notion that contradictions are not problems that an individual is not unilateral, but plural. In this paper, we investigate how philosophies of pluralism can inform our understanding of impossibility of identity in classroom curriculum and pedagogy.

Keywords: identity, gender, culture, pluralism, education, philosophy of education, queer theory, philosophy of mind, adolescent development

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Authors: Mohammed Husein Mohammad Rashid

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For a bounded linear operator T acting on a complex infinite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators.

Keywords: fuglede-putnam theorem, normal operators, ∗-class a operators, dominant operators

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Authors: Jason Clarke, Michaela Porubanova, Angela Mazzoli, Gulsah Kut

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What accounts for our perception that time inexorably passes in one direction, from the past to the future, the so-called arrow of time, given that the laws of physics permit motion in one temporal direction to also happen in the reverse temporal direction? Modern physics says that the reason for time’s unidirectional physical arrow is the relationship between time and entropy, the degree of disorder in the universe, which is evolving from low entropy (high order; thermal disequilibrium) toward high entropy (high disorder; thermal equilibrium), the second law of thermodynamics. Accordingly, our perception of the direction of time, from past to future, is believed to emanate as a result of the natural evolution of entropy from low to high, with low entropy defining our notion of ‘before’ and high entropy defining our notion of ‘after’. Here we explored this proposed relationship between entropy and the perception of time’s arrow. We predicted that if the brain has some mechanism for detecting entropy, whose output feeds into processes involved in constructing our perception of the direction of time, presentation of violations to the expectation that low entropy defines ‘before’ and high entropy defines ‘after’ would alert this mechanism, leading to measurable behavioral effects, namely a disruption in duration perception. To test this hypothesis, participants were shown briefly-presented (1000 ms or 500 ms) computer-generated visual dynamic events: novel 3D shapes that were seen either to evolve from whole figures into parts (low to high entropy condition) or were seen in the reverse direction: parts that coalesced into whole figures (high to low entropy condition). On each trial, participants were instructed to reproduce the duration of their visual experience of the stimulus by pressing and releasing the space bar. To ensure that attention was being deployed to the stimuli, a secondary task was to report the direction of the visual event (forward or reverse motion). Participants completed 60 trials. As predicted, we found that duration reproduction was significantly longer for the high to low entropy condition compared to the low to high entropy condition (p=.03). This preliminary data suggests the presence of a neural mechanism that detects entropy, which is used by other processes to construct our perception of the direction of time or time’s arrow.

Keywords: time perception, entropy, temporal illusions, duration perception

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Authors: M. Chaichanyut, S. Tungjitkusolmun

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This research is presented with microwave (MW) ablation by using the T-Prong monopole antennas. In the study, three-dimensional (3D) finite-element methods (FEM) were utilized to analyse: the tissue heat flux, temperature distributions (heating pattern) and volume destruction during MW ablation in liver cancer tissue. The configurations of T-Prong monopole antennas were considered: Three T-prong antenna, Expand T-Prong antenna and Arrow T-Prong antenna. The 3D FEMs solutions were based on Maxwell and bio-heat equations. The microwave power deliveries were 10 W; the duration of ablation in all cases was 300s. Our numerical result, heat flux and the hotspot occurred at the tip of the T-prong antenna for all cases. The temperature distribution pattern of all antennas was teardrop. The Arrow T-Prong antenna can induce the highest temperature within cancer tissue. The microwave ablation was successful when the region where the temperatures exceed 50°C (i.e. complete destruction). The Expand T-Prong antenna could complete destruction the liver cancer tissue was maximized (6.05 cm³). The ablation pattern or axial ratio (Widest/length) of Expand T-Prong antenna and Arrow T-Prong antenna was 1, but the axial ratio of Three T-prong antenna of about 1.15.

Keywords: liver cancer, T-Prong antenna, finite element, microwave ablation

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Authors: Yu Lu

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Fixed point theory is a basic tool for the study of the existence of Nash equilibria in game theory. This paper presents a significant generalization of the Veinott-Zhou fixed point theorem for increasing correspondences, which serves as an essential framework for investigating the existence of Nash equilibria in supermodular and quasisupermodular games. To establish our proofs, we explore different conceptions of multivalued increasingness and provide comprehensive results concerning the existence of the largest/least fixed point. We provide two distinct approaches to the proof, each offering unique insights and advantages. These advancements not only extend the applicability of the Veinott-Zhou theorem to a broader range of economic scenarios but also enhance the theoretical framework for analyzing equilibrium behavior in complex game-theoretic models. Our findings pave the way for future research in the development of more sophisticated models of economic behavior and strategic interaction.

Keywords: fixed-point, Tarski’s fixed-point theorem, Nash equilibrium, supermodular game

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

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Authors: Chia-Chen Wu, Chih-Fu Wu, Pey-Weng Lien, Kai-Chieh Lin

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In the past, the most comprehensively adopted light source was incandescent light bulbs, but with the appearance of LED light sources, traditional light sources have been gradually replaced by LEDs because of its numerous superior characteristics. However, many of the standards do not apply to LEDs as the two light sources are characterized differently. This also intensifies the significance of studies on LEDs. As a Kansei design study investigating the visual glare produced by traffic arrows implemented with LEDs, this study conducted a semantic analysis on the styles of traffic arrows used in domestic and international occasions. The results will be able to reduce drivers’ misrecognition that results in the unsuccessful arrival at the destination, or in traffic accidents. This study started with a literature review and surveyed the status quo before conducting experiments that were divided in two parts. The first part involved a screening experiment of arrow samples, where cluster analysis was conducted to choose five representative samples of LED displays. The second part was a semantic experiment on the display of arrows using LEDs, where the five representative samples and the selected ten adjectives were incorporated. Analyzing the results with Quantification Theory Type I, it was found that among the composition of arrows, fletching was the most significant factor that influenced the adjectives. In contrast, a “no fletching” design was more abstract and vague. It lacked the ability to convey the intended message and might bear psychological negative connotation including “dangerous,” “forbidden,” and “unreliable.” The arrow design consisting of “> shaped fletching” was found to be more concrete and definite, showing positive connotation including “safe,” “cautious,” and “reliable.” When a stimulus was placed at a farther distance, the glare could be significantly reduced; moreover, the visual evaluation scores would be higher. On the contrary, if the fletching and the shaft had a similar proportion, looking at the stimuli caused higher evaluation at a closer distance. The above results will be able to be applied to the design of traffic arrows by conveying information definitely and rapidly. In addition, drivers’ safety could be enhanced by understanding the cause of glare and improving visual recognizability.

Keywords: LED, arrow, Kansei research, preferred imagery

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Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu

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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC_4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC₃ cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC_4,6 cryptosystem than LUC₃ and LUC cryptosystems. Current study concludes that LUC_4,6 cryptosystem is more secure than LUC and LUC₃ cryptosystems in sustaining against Lenstra’s attack.

Keywords: Lucas sequence, Dickson polynomial, faulty signature, corresponding signature, congruence

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Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Paola Cattabriga

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According to Gödel’s first incompleteness argument it is possible to construct a formally undecidable proposition in Principia mathematica, a statement that, although true, turns out to be neither provable nor refutable for the system, making therefore incomplete any formal system suitable for the arithmetic of integers. Its features and limitation effects are today widespread basics throughout whole scientific thought. This article brings Gödel’s achievement into question by the definition of the refutability predicate as a number-theoretical statement. We develop proof of invalidity of Theorem VI in Gödel’s 1931, the so-called Gödel’s first incompleteness theorem, in two steps: defining refutability within the same recursive status as provability and showing that as a consequence propositions (15) and (16), derived from definition 8.1 in Gödel’s 1931, are false and unacceptable for the system. The achievement of their falsity blocks the derivation of Theorem VI, which turns out to be therefore invalid, together with all the depending theorems. This article opens up thus new perspectives for mathematical research and for the overall scientific reasoning.

Keywords: Gödel numbering, incompleteness, provability predicate, refutability predicate

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Authors: Mukhtari Hussaini Muhammad, Abba Adamu

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The paper will examine the approaches and solutions that will be offered by Senior Secondary School II Students (Demonstration Secondary School, Azare Bauchi State Northern Nigeria – Hausa/ Fulani predominant area) toward solving exercises related to the circle theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of the circumference. The Students will be divided in to 2 groups by given them numbers 1, 2; 1, 2; 1, 2, then all 1s formed group I and all 2s formed group II. Group I will be considered as control group in which the traditional method will be applied during instructions. Thus, the researcher will revise the concept of circle, state the theorem, prove the theorem and then solve examples. Group II, experimental group in which the concept of circle will be revised to the students and then the students will be asked to draw different circles, mark arcs, draw angle at the center, angle at the circumference then measure the angles constructed. The students will be asked to explain what they can infer/deduce from the angles measured and lastly, examples will be solved. During the next contact day, both groups will be subjected to solving exercises in the classroom related to the theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of circumference. The solution to the exercises will be marked, the scores compared/analysed using relevant statistical tool. It is expected that group II will perform better because of the method/ technique followed during instructions is more learner-centered. By exploiting the talents of the individual learners through listening to the views and asking them how they arrived at a solution will really improve learning and understanding.

Keywords: circle theorem, control group, experimental group, traditional method

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Authors: Hemant Kumar Pathak

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In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: Ti-Jun Xiao, Zhe Xu

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Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem.

Keywords: evolutional control system, controllability, boundary control, existence and uniqueness

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Authors: D. S. Palimkar

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Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Ather Saeed, Arif Khan, Jeffrey Gosper

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Sensor devices are prone to errors and sudden node failures, which are difficult to detect in a timely manner when deployed in real-time, hazardous, large-scale harsh environments and in medical emergencies. Therefore, the loss of data can be life-threatening when the sensed phenomenon is not disseminated due to sudden node failure, battery depletion or temporary malfunctioning. We introduce a set of partial differential equations for localizing faults, similar to Green’s and Maxwell’s equations used in Electrostatics and Electromagnetism. We introduce a node organization and clustering scheme for self-stabilizing sensor networks. Green’s theorem is applied to regions where the curve is closed and continuously differentiable to ensure network connectivity. Experimental results show that the proposed GTFD (Green’s Theorem fault-detection and Self-stabilization) protocol not only detects faulty nodes but also accurately generates network stability graphs where urgent intervention is required for dynamically self-stabilizing the network.

Keywords: Green’s Theorem, self-stabilization, fault-localization, RSSI, WSN, clustering

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Muhammad Sufian Jusoh, Mesliza Mohamed

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In this paper, we investigate the existence of positive solutions for a Dirichlet second order boundary value problem by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Keywords: Krasnosel'skii fixed point theorem, positive solutions, Dirichlet boundary value problem, Dirichlet second order boundary problem

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Authors: Khushboo Gokani, Renu Josan

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Mahasweta Devi and Toni Morrison are the two stalwarts of the Indian-English and the Afro-American literature respectively. The writings of these two novelists are authentic and powerful records of the lives of the people because much of their personal experiences have gone into the making of their works. Devi, a representative force of the Indian English literature, is also a social activist working with the tribals of Bihar, Jharkhand, Orissa and West Bengal. Most of her works echo the lives and struggles of the subalterns as is evident in her 'best-beloved book' Chotti Munda and His Arrow. The novelist focuses on the struggle of the tribals against the colonial and the feudal powers to create their identity, thereby, embarking on the ideological project called Setting the Record Straight. The Nobel laureate Toni Morrison, on the other hand, brings to the fore the crucial issues of gender, race, and class in many of her significant works. In one of her representative works, Sula, the protagonist emerges as a non-conformist and directly confronts the notion of a ‘good woman’ nurtured by the community of the Blacks. In addition to this, the struggle of the Blacks against the White domination, also become an important theme of the text. The thrust of the paper lies in making a critical analysis of the portrayal of the heroic attempts of the subaltern protagonist and the artistic endeavor of the novelists in challenging the stereotypes.

Keywords: the struggle of the muted groups, subaltern, center and periphery, challenging the stereotypes

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Authors: Anas M. Fares

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Reinforced concrete shear walls are the most frequently used forms of lateral resisting structural elements. These walls may take many forms due to their functions and locations in the building. In Palestine, the most lateral resisting forces construction forms is the cantilever shear walls system. It is thus of prime importance to study the rigidity of these walls. The virtual work theorem is used to derive the total lateral deflection of cantilever shear walls due to flexural and shear deformation. The case of neglecting the shear deformation in the walls is also studied, and it is found that the wall height to length aspect ratio (H/B) plays a major role in calculating the lateral deflection and the rigidity of such walls. When the H/B is more than or equal to 3.7, the shear deformation may be neglected from the calculation of the lateral deflection. Moreover, the walls with the same material properties, same lateral load value, and same aspect ratio, shall have the same of both the lateral deflection and the rigidity. Finally, an equation to calculate the total rigidity and total deflection of such walls is derived by using the virtual work theorem for a cantilever beam.

Keywords: cantilever shear walls, flexural deformation, lateral deflection, lateral loads, reinforced concrete shear walls, rigidity, shear deformation, virtual work theorem

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Peter Akayuure, Michael Johnson Nabie

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Similar to many colonized nations in the world, one indelible mark left by colonial masters after Ghana’s independence in 1957 has been the fact that many contexts used to teach statistics and probability concepts are often alien and do not resonate with the social domain of our indigenous Ghanaian child. This has seriously limited the understanding, discoveries, and applications of mathematics for national developments. With the recent curriculum demands of making the Ghanaian child mathematically literate, this qualitative study involved video recordings and mathematical analysis of play sessions of an indigenous girl game called Ampe with the aim to demystify the concepts in probability theorem, which is applied in mathematics related fields of study. The mathematical analysis shows that the game of Ampe, which is widely played by school girls in Ghana, is suitable for learning concepts of the probability theorems. It was also revealed that as a girl game, the use of Ampe provides good lessons to educators, textbook writers, and teachers to rethink about the selection of mathematics tasks and learning contexts that are sensitive to gender. As we undertake to transform teacher education and student learning, the use of indigenous games should be critically revisited.

Keywords: Ampe, mathematical analysis, probability theorem, Ghanaian girl game

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Authors: Zainab Magaji Musa, Nordin M. A. Rahman, Julaily Aida Jusoh

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The web services applications for digital reference service (WSDRS) of LIS model is an informal model that claims to reduce the problems of digital reference services in libraries. It uses web services technology to provide efficient way of satisfying users’ needs in the reference section of libraries. The formal WSDRS model consists of the Z specifications of all the informal specifications of the model. This paper discusses the formal validation of the Z specifications of WSDRS model. The authors formally verify and thus validate the properties of the model using Z/EVES theorem prover.

Keywords: validation, verification, formal, theorem prover

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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