Search results for: verication theorem

Authors: Yuyang Cheng, Marcos Escobar-Anel

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This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Keywords: stochastic covariance process, 4/2 stochastic volatility model, stochastic co-volatility movements, characteristic function, expected utility theory, verication theorem

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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: 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: Noor Ul Afsar, Wengen Ji, Bin Wu, Muhammad A. Shehzad, Liang Ge, Tongwen Xu

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The synthesis of monovalent cation perm-selective membranes (MCPMs) to efficiently discriminate amongst cations from seawater is of great importance for several industrial applications. However, a technical approach is highly desired to construct MCPMs to obtain a high ionic flux and sustain perm-selectivity simultaneously. In the present work, the thickness of the quaternized poly (2, 6-dimethyl-1, 4-phenylene oxide) (QPPO) layer on the surface of the SPPO-PVA (SPVA) composite membrane was adjusted using a facile procedure to achieve high permselectivity without scarifying the ionic flux. The thickness of the selective layer was precisely controlled using various concentrations of the QPPO solution. By the introduction of the cationic layer on the SPVA membrane, the monovalent cation can be separated from the divalent cation by their difference in charge density. The influence of the selective barrier (thickness) endows MCPMs with high perm-selectivity up to 12.7 for 0.1 mol L⁻¹ Li⁺/Mg²⁺ system, which is very satisfactory for polymeric membranes. The fabricated membranes have low electrical resistance and high limiting current density (iₗᵢₘ). Keeping in view the ED results, the prepared membranes with selective surface layers could be a viable candidate for Li⁺ selective separation from divalent cation Mg²⁺.

Keywords: monovalent cation perm-selective membranes, cation fractionation, perm-selectivity, ionic flux, electrodialysis

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Authors: G. S. Sudha, Smita Mohanty, S. K. Nayak

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Epoxidized oils can replace petroleum derived materials in numerous industrial applications, because of their respectable oxirane oxygen content and high reactivity of oxirane ring. Epoxidized castor oil (ECO) has synthesized in the presence of a sulphonated polystyrene type cation exchange resin. The formation of the oxirane ring was confirmed by Fourier Transform Infrared Spectroscopy (FTIR) analysis. The epoxidation reaction was evaluated by Nuclear Magnetic Resonance (NMR) studies. ECO is used as a toughening phase to increase the toughness of petroleum-based epoxy resin.

Keywords: epoxy resin, epoxidized castor oil, sulphonated polystyrene type cation exchange resin, petroleum derived materials

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Authors: J. P. Borah, R. D. Raland

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Hyperthermia is one of many techniques used destroys cancerous cell. It uses the physical methods to heat certain organ or tissue delivering an adequate temperature in an appropriate period of time, to the entire tumor volume for achieving optimal therapeutic results. Magnetic Metal ferrites nanoparticles (MFe₂O₄ where M = Mn, Zn, Ni, Co, Mg, etc.) are one of the most potential candidates for hyperthermia due to their tunability, biocompatibility, chemical stability and notable ability to mediate high rate of heat induction. However, to obtain the desirable properties for these applications, it is important to optimize their chemical composition, structure and magnetic properties. These properties are mainly sensitive to cation distribution of tetrahedral and octahedral sites. Among the ferrites, zinc ferrite (ZnFe₂O₄) and Manganese ferrite ((MnFe₂O₄) is one of a strong candidate for hyperthermia application because Mn and zinc have a non-magnetic cation and therefore the magnetic property is determined only by the cation distribution of iron, which provides a better platform to manipulate or tailor the properties. In this talk, influence of doping and surfactant towards cation re-distribution leading to an enhancement of magnetic properties of ferrite nanoparticles will be demonstrated. The efficiency of heat generation in association with the enhanced magnetic property is also well discussed in this talk.

Keywords: magnetic nanoparticle, hyperthermia, x-ray diffraction, TEM study

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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: Y. H. Hwang, J. Won, Y. S. Kang

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Since ionic liquids have a special interaction with gas specially CO2 and/or olefin, supported ionic liquids membrane (SILM) are fabricated for practical gas separation. However, SILM has a problem in practical application due to the low mechanical stability under high pressure for gas separation. In order to improve the mechanical strength of the selective ionic liquid layer, we prepared supported ion gel membrane by the formation of gel on the surface of Nylon support. The ion gel was prepared by the addition of poly(styrene-block-ethyleneoxide-block-styrene) triblock copolymer in four tricyanomethanide ionic liquids have different cation; 1-ethyl-3-methlyimidazolium tricyanomethanide, 1-butyl-3-methlyimidazolium tricyanomethanide, 1-butyl-1-methylpyrrolidinium tricyanomethanide, 1-butyl-4-methylpyridinium tricyanomethanide using methylenechloride as a solvent. The characters of ion gel with different cation were studied. Four different gases (CO2, N2, O2, and CH4) permeance were measured at room temperature by bubble flow meter and cation effect of tricyanomethanide ionic liquids investigated.

Keywords: membrane, ionic liquid, ion gel, nanostructure

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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: 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: V. Pérez-Herranz, M. Pinel, E. M. Ortega, M. García-Gabaldón

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In the present work, Electrochemical Impedance Spectrocopy (EIS) is applied to study the transport of different metal cations through a cation-exchange membrane. This technique enables the identification of the ionic-transport characteristics and to distinguish between different transport mechanisms occurring at different current density ranges. The impedance spectra are dependent on the applied dc current density, on the type of cation and on the concentration. When the applied dc current density increases, the diameter of the impedance spectra loops increases because all the components of membrane system resistance increase. The diameter of the impedance plots decreases in the order of Na(I), Ni(II) and Cr(III) due to the increased interactions between the negatively charged sulfonic groups of the membrane and the cations with greater charge. Nyquist plots are shifted towards lower values of the real impedance, and its diameter decreases with the increase of concentration due to the decrease of the solution resistance.

Keywords: ion-exchange membranes, Electrochemical Impedance Spectrocopy, multivalent metal cations, membrane system

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Authors: Yichao Liang, Biye Chen, Xiang Li, Steven R. Dimler

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This study investigated the effects of adding calcium and magnesium chloride on heat and storage stability of milk protein concentrate-soy protein isolate (8:2 respectively) mixtures containing 10% w/w total protein subjected to the in-container sterilization (115 °C x 15 min). The particle size does not change when emulsions are heated at pH between 6.7 and 7.3 irrespective of the mixed protein ratio. Increasing concentration of divalent cation salts resulted in an increase in protein particle size, dry sediment formation and sediment height and a decrease in pH, heat stability and hydration in milk protein concentrate-soy protein isolate mixtures solutions on sterilization at 115°C. Fortification of divalent cation salts in milk protein concentrate-soy protein isolate mixture solutions resulted in an accelerated protein sedimentation and two unique sediment regions during accelerated storage stability testing. Moreover, the heat stability decreased upon sterilization at 115°C, with addition of MgCl₂ causing a greater increase in sedimentation velocity and compressibility than CaCl₂. Increasing pH value of protein milk concentrate-soy protein isolate mixtures solutions from 6.7 to 7.2 resulted in an increase in viscosity following the heat treatment. The study demonstrated that the type and concentration of divalent cation salts used strongly impact heat and storage stability of milk protein concentrate-soy protein isolate mixture nutritional beverages.

Keywords: divalent cation salts, heat stability, milk protein concentrate, soy protein isolate, storage stability

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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: Hakan Gungunes, Ismail A. Auwal, Abdulhadi Baykal, Sagar E. Shirsath

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Barium hexaferrite, BaFe₁₂O₁₉, substituted by Bi³⁺ and La³⁺ (BaBiₓLaₓFe₁₂₋₂ₓO₁₉ where 0.0 ≤ x ≤ 0.5) were prepared by solid state synthesis route. The effect of substituted Bi³⁺ and La³⁺ ions on the structure, morphology, magnetic and cation distributions of barium hexaferrite were investigated by X-ray powder diffractometry (XRD), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), Fourier transform infrared spectroscopy (FT-IR) and Mössbauer spectroscopy. XRD powder patterns were refined by the Rietveld analysis method which confirmed the formation of single phase magneto-plumbite structure and the substitution of La³⁺ and Bi³⁺ ions into the lattice of barium ferrite. These results show that both La³⁺ and Bi³⁺ ions completely enter into barium hexaferrite lattice without disturbing the hexagonal ferrite structure. The EDX spectra confirmed the presence of all the constituents in expected elemental percentage. From 57Fe Mössbauer spectroscopy data, the variation in line width, isomer shift, quadrupole splitting and hyperfine magnetic field values on Bi and La substitutions have been determined. Cation distribution in the presently investigated hexaferrite system was estimated using the relative area of Mössbauer spectroscopy.

Keywords: hexaferrite, mössbauer, cation distribution, solid state synthesis

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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: Reira Kinoshita, Shin'ichi Ishimaru

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Vapochromism is a type of chromism in which the color of a substance changes when it is exposed to the vapor of volatile materials, and has been investigated for the application of chemical sensors for volatile organic compounds causing sick building syndrome and health hazards in workspaces. We synthesized intercalation compounds of 3,3',5,5'-tetramethylbenzidine (TMB), and tetrasilisicfluormica (TSFM) by the commonly used cation-exchange method with the cation ratio TMB²⁺/CEC of TSFM = 1.0, 2.0, 2.7 and 5.4 to investigate the vapochromism of these materials. The obtained samples were characterized by powder XRD, XRF, TG-DTA, N₂ adsorption, and SEM. Vapochromism was measured for each sample under a controlled atmosphere by a handy reflectance spectrometer directly from the outside of the glass sample tubes. The color was yellow for all specimens vacuum-dried at 50 °C, but it turned green under H₂O vapor exposure for the samples with TMB²⁺/CEC = 2.0, 2.7, and 5.4 and blue under acetonitrile vapor for all cation ratios. Especially the sample TMB²⁺/CEC = 2.0 showed clear chromism both for water and acetonitrile. On the other hand, no clear color change was observed for vapors of alcohols, acetone, and non-polar solvents. From these results, this material can be expected to apply for easy detection of humidity and acetonitrile vapor in the environment.

Keywords: chemical sensor, intercalation compound, tetramethylbenzidine, tetrasilisicfluormica, vapochromism, volatile organic compounds

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Authors: A. Alshebani, Y. Swesi, S. Mrayed, F. Altaher, I. Musbah

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Cs-type nanocomposite zeolite membrane was successfully synthesized on an alumina ceramic hollow fibre with a mean outer diameter of 1.7 mm; cesium cationic exchange test was carried out inside test module with mean wall thickness of 230 μm and an average crossing pore size smaller than 0.2 μm. Separation factor of n-butane/H2 obtained indicate that a relatively high quality closed to 20. Maxwell-Stefan modeling provides an equivalent thickness lower than 1 µm. To compare the difference an application to CO2/N2 separation has been achieved, reaching separation factors close to (4,18) before and after cation exchange on H-zeolite membrane formed within the pores of a ceramic alumina substrate.

Keywords: MFI membrane, nanocomposite, ceramic hollow fibre, CO2, ion-exchange

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Authors: A. Alshebani, Y. Swesi, S. Mrayed, F. Altaher, I. Musbah

Abstract:

Cs-type nanocomposite zeolite membrane was successfully synthesized on a alumina ceramic hollow fibre with a mean outer diameter of 1.7 mm, cesium cationic exchange test was carried out inside test module with mean wall thickness of 230 μm and an average crossing pore size smaller than 0.2 μm. Separation factor of n-butane/H2 obtained indicate that a relatively high quality closed to 20. Maxwell-Stefan modeling provides an equivalent thickness lower than 1 µm. To compare the difference an application to CO2/N2 separation has been achieved, reaching separation factors close to (4,18) before and after cation exchange on H-zeolite membrane formed within the pores of a ceramic alumina substrate.

Keywords: MFI membrane, CO2, nanocomposite, ceramic hollow fibre, ion-exchange

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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: 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: Ahmed O. Apampa, Yinusa A. Jimoh

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The paper examines the mechanism of pozzolan-soil reactions, using a recent study on the chemical stabilization of a Class A-2-7 (3) lateritic soil, with corn cob ash (CCA) as case study. The objectives are to establish a nexus between cation exchange capacity of the soil, the alkaline forming compounds in CCA and percentage CCA addition to soil beyond which no more improvement in strength properties can be achieved; and to propose feasible chemical reactions to explain the chemical stabilization of the lateritic soil with CCA alone. The lateritic soil, as well as CCA of pozzolanic quality Class C were separately analysed for their metallic oxide composition using the X-Ray Fluorescence technique. The cation exchange capacity (CEC) of the soil and the CCA were computed theoretically using the percentage composition of the base cations Ca²⁺, Mg²⁺ K⁺ and Na²⁺ as 1.48 meq/100 g and 61.67 meq/100 g respectively, thus indicating a ratio of 0.024 or 2.4%. This figure, taken as the theoretical amount required to just fill up the exchangeable sites of the clay molecules, compares well with the laboratory observation of 1.5% for the optimum level of CCA addition to lateritic soil. The paper went on to present chemical reaction equations between the alkaline earth metals in the CCA and the silica in the lateritic soil to form silicates, thereby proposing an extension of the theory of mechanism of soil stabilization to cover chemical stabilization with pozzolanic ash only. The paper concluded by recommending further research on the molecular structure of soils stabilized with pozzolanic waste ash alone, with a view to confirming the chemical equations advanced in the study.

Keywords: cation exchange capacity, corn cob ash, lateritic soil, soil stabilization

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