Waves are more responsive to the wind blowing over the surface of the water. While wind moving over the water surface imparts its kinetic energy to the underlying water body due to friction and drag force. In this present study introducing new tool for wave forecast in coastal areas during extreme events, it is accurately predicting wave heights by giving distance of the extreme event and wind speed as input to this. This new tool is definitely most helpful for coastal areas for Maintenance of harbours, ship-routing, offshore platforms, coastal livelihood, coastal processes and many more marine engineering applications. This is successfully tested for coastal area of India and giving validation results for the accuracy of the tool. These WAVEFORT tool predicted wave heights are compared with the real time measured in-situ observations of shallow water Directional Wave Rider Buoy (DWRB) data off coastal area of India in 15m depth. Even in high wave conditions also this tool predicted wave accurately with correlation coefficient value of 0.95 tells the accuracy of the tool. The complete validation results of the WAVEFORT tool are discussed on this present study. KEY WORDS: Wave model, Cyclone forecast and Coastal areas

La valutazione delle emissioni odorigene e dei relativi impatti viene effettuata utilizzando i fattori di emissioni di odori (OEF), cosi come riportato in numerosi studi scientifici, che tengono conto solo della capacità dell'impianto per la quantificazione dell’indice di attività.Le attività di ricerca, presenti in questo studio, sono state improntate all’individuazione delle principali fonti di odori e le loro relative concentrazioni ed emissioni provenienti da un grande Impianto di Trattamento Integrato Anaerobico-Aerobico. Tali fonti di odori sono state valutate attraverso l’ofattometria dinamica.Gli OEF rilevanti sono stati stimati utilizzando un set di dati sperimentali e confrontati con quelli teorici proposti negli studi di letteratura su impianti di trattamento simili.I risultati hanno mostrato come le principali emissioni di odori sono associate al processo di compostaggio.

Reduction in the torsional vibration of heavy rotors like turbo-generator rotor is important for the safe and efficient functioning of the power plant. In this paper theoretical study is performed to control the torsional vibration in the turbo-generator rotor using piezoelectric material as sensor and actuator. Polyvinylidene fluoride (PVDF) layer is used as sensor and actuator. Proportional and velocity feedback is used as control law. The variation in the electromagnetic torque of synchronous generator during various electrical faults is evaluated using dq0 model. Finite element method is used to model the rotor elements. The coupled equations are solved in MATLAB using Newmark-beta integration method. The coupling elements of turbine and generator are most susceptible to the shear failure so torsional vibration of coupled rotor on coupling elements are compare for controlled and uncontrolled scenario. Simulation results show that for actively controlled rotor significant reduction in the amplitude of torsional vibrations is observed.

The paper presents a novel technique to detect the solvents in water like sugar, salt, and its combination using a wideband CPW fed microstrip antenna with periodic EBG ground structure. The antenna is designed and fabricated to operates at the bandwidth of 3 GHz with a stable gain of 9 dBi maintaining VSWR<2. The uniquely designed antenna works as a sensor in its near field to sense the solvents in water in terms of resonant frequency and reflection method in wider bandwidth. The technique also detects the changes in the temperature of the soft drinks as a function of reflection characteristics. This technique will be useful for finding the percentage of solvents in soft drinks before consumption. The sensing technique is without physical contact with the solution and chemical process. Therefore it is a healthy way to find the ingredients in solutions like soft drinks. The technique will be useful to the food regulation boards to limit the contents of beverages and cold drinks.

I VOCs, Volatile Organic Compounds, sono tra gli inquinanti principali che generano impatto da odori. Si definisce inquinante una sostanza che procura danni alla salute umana, nonché all’ambiente stesso: i danni principali sono legati alla tossicità delle emissioni, nonché a sintomi quali mal di testa, nausea e problemi respiratori. Le principali fonti dalle quali possono provenire i VOCs sono: industrie, impianti di trattamento delle acque reflue, compostaggio e trattamento rifiuti. Risulta di grande importanza capire come abbattere queste sostanze: in particolare, ci si è concentrati sull’abbattimento del toluene, uno dei principali VOCs, mediante tecniche di ossidazione avanzata UV/O3, attraverso un esperimento in scala di laboratorio. Inoltre, viene presentata una tecnica biologica di abbattimento del toluene (BTF), risultata ecosostenibile anche in termini di riduzioni di emissioni di CO2, grazie all'interazione tra microalghe e batteri. Sono state poi analizzate anche altre tecniche tra cui la pervaporazione su membrana, un processo termico di separazione su membrana che permette la rimozione di particolari sostanze organiche, tra cui il toluene, attraverso l'utilizzo di membrane porose che presentano elevate affinità di permeabilità nella rimozione dei VOCs.  Si è riscontrato, infine, che l’efficacia dei trattamenti di ossidazione avanzata sia notevole anche per altri microinquinanti, per cui è possibile pensare di poterli applicare ad ampio spettro, anche per prevenire danni all’ecosistema stesso. 

In this paper we present design of RTL-SDR based low cost receiver for meteorological balloon telemetry. In developed receiver all the demodulation processes are performed in software developed in LabVIEW. Design and fabrication of Quarter Wave Monopole Antenna and Quadrifilar Helix Antenna (QHA) is also presented for use with the receiver. Antennas are selected such that the combined beam pattern provides optimum coverage in both low and high elevation angles. This system is designed to operate in meteorological-aids frequency band of 400-406 MHz. Paper presents bit error rate performance of developed receiver. Performances of the RTL-SDR receiver using both the antennas are assessed by processing the signals received from the radiosonde flights at Gadanki (13.46°N, 79.17°E). Finally it is shown that RTL-SDR based receiver can receive signals up to the range of about 75-80 Km.

Investigating the causes and consequences of differential migration may help us understand possible variability in resilience to environmental change within species and populations. Inter-individual variation in temperament has been recognised as a major driver of population ecology, but its relationship to migratory strategy has been ill-explored. Here, we investigated whether male migrant and resident Cory’s Shearwaters (Calonectris borealis), a long-lived partially migratory seabird, are distinguishable by their temperament at the colony. We tracked over 100 individuals overwinter using GLS devices and assessed whether exploratory behaviour and reaction to extraction from the nest corresponded to migratory strategy over a period of two years. While exploratory behaviour was unrelated to migratory strategy, birds that were more reactive towards extraction from the nest were more likely to migrate. This, together with previous findings that migrants display higher physiological stress over winter, suggests that migrants and residents may be distinguishable by their stress threshold.

The ultimate goal of this work is to find a region where the response surface of a function that is not well characterized in terms of optimality resembles one that is well-characterized in such terms to find, at least, a local optimum. The region in the functions’ input space where this resemblance occurs, we call a Window of Maximal Similarity (WMS) and is identified by formulating and solving an optimization problem. The method is one of minimization of squared errors and can be used to explore experimental, or simulated data. A series of examples, that include several typical global optimization test functions in literature, are presented in order to demonstrate the method’s feasibility and capability for generating a two-dimensional WMS. This tool is a viable element that will serve for the future development of Optimization by Similarity.

Background NOD-like receptor pyrin 7 (NLRP7) has been identified as the major gene responsible for the recurrent hydatidiform mole (RHM). The immunological role of NLRP7 mutation in HM patients has not been conclusively demonstrated. Hence, we aim to demonstrate this role in our study. Methods We followed 12 new patients with NLRP7 nonsynonymous variations (NSVs) from date to date. Peripheral blood mononuclear cells (PBMCs) were collected from patients with and without NLRP7 mutation, separately. Supernatant IL-1β secretion, intracellular pro-IL-1β and mature-IL-1β expressions were measured after 24h lipopolysaccharide (LPS) stimulation. Plasmids with corresponding NSVs were generated to evaluate the ability of processing pro-IL-1β into mature-IL-1β in vitro. Results Homozygous or compound heterozygous NLRP7 mutation secreted less IL-1β in root of abnormal intracellular pro-IL-1β or mature-IL-1β according to different domain defective. Plasmids with NSVs could also affect processing or/and trafficking together with caspase-1 and apoptosis-associated speck-like protein (ASC). Conclusion Inflammasome related NLRP7 mutation is a potential mechanism of RHM.

In this paper, we provide an efficient numerical technique based on the Bernstein polynomials for numerical approximation of the coupled Lane-Emden type equation which arises in various fields of applied mathematics, physical and chemical sciences. We consider the equivalent integral form of the coupled Lane-Emden boundary value problems. The Bernstein collocation method is used to convert the integral equation into a system of nonlinear equations. This system is then solved efficiently by suitable iterative method. The error analysis of the current method is discussed. The accuracy of the proposed method is examined by calculating the maximum absolute error $L_{\infty}$, the $L_{2}$ error and the residual error of some numerical examples. The obtained numerical results are compared with the exact solutions and the results obtained by the other known techniques.

The set of hybrid numbers is a noncommutative number system unified and generalized the complex, dual and double(hyperbolic) numbers with the relation IH = − HI = ε + I. Two hybrid numbers P and Q are said to be similar if there exist a hybrid number X satisfying the equality X−1QX = P. And it is denoted by p ∼ q. In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations PX = XQ and QX − XP = C for P, Q, C ∈ 𝕂. KEYWORDS : Hybrid numbers, quaternions, coquaternions, dual and double numbers. MSC CLASSIFICATION : 15A66, 11R52, 15A18, 15A06, 16S50.

Asthma is a chronic inflammatory disease of the airways, which is considered to be mediated by the allergen-specific CD4+ T cells, Th2 cytokines, and allergen-specific IgE antibodies to play a key role in the initiation and perpetuation of chronic airway inflammation. The most common clinical manifestations of asthma are characterized by airway inflammation, airway obstruction, airway hyperresponsiveness, and airway microvascular remodeling. In addition to inflammatory cells, a tiny population of T regulatory cells (Tregs) control immune homeostasis, suppress allergic responses and participate in the resolution of inflammation-associated tissue injuries. Preclinical studies from animal models have demonstrated the huge therapeutic potential of Tregs in asthma conditions. Increasing evidence indicates that Tregs could be used to inhibit pathogenic asthma inflammation, and airway microvascular remodeling during the progression of asthma. This review addresses the relationship between locally accumulated Tregs and the development of asthmatic inflammation, and associated airway remodeling during the disease progression.

1. Introduction Phage display technology was first introduced by George P. Smith, who integrated protein coding fragments into filamentous bacteriophage M13 and the process of selection of desired protein fragment was named as panning [1].  Phage display is an inexpensive technology exploited for exogenous peptides, aiding increased target affinity and interaction [2]. It integrates the principles of genetic engineering with combinatorial chemistry. In general, phage display is composed of a system where exogenous DNA is interested in a filamentous phage genome along with the phage coat encoding sequence. Expression leads to the phage particles that express the sequence of interest in fusion with on the coat protein. These sequences are capable of interacting with various external targets/ligands. One of the significant characteristics of phage display is the production of large number of libraries and hence, these libraries can be used for the determination of the functional peptides with desired properties [3]. Proteins, peptides and antigens depend on the conformational changes to attain complete structural and functional characteristics. Immunization methods are barrier to this whereas, phage display method can be used to determine peptides and antigens for several ranges of epitopes and peptides [1]. M13 bacteriophage is the most commonly used phages for the purpose, owing to its flexible cylindrical protein structure and a large number of coat proteins including pIII, pVI, pVIII,pVII and pIX. pIII coat protein is responsible for the attachment of the bacteriophage virus to the pilus of the bacteria. After the attachment of pIII to the membrane protein, the genome of the phage is transferred into the bacteria where it is converted into a double stranded DNA and synthesis of new proteins occur around single stranded phage genome. The final phage particles are extruded from the bacteria, however, M13 phages do not kill the bacteria and remain in the constant phase of infection and growth [4]. The basic process of phage display is summarized in figure 1.        1.1 Natural and synthetic peptide library: In term of peptides, phage libraries are either composed of natural peptides or synthetic ones. Natural peptide libraries are constructed by extracting DNA fragments from the organism (example: mice) and inserting it into the phage particle. As a result, phage particles, on their surface, express natural peptides. However, synthetic libraries are composed of cloned synthetic and randomly generated oligomeric sequences inserted into the phage genome [4]. 1.2 Antibodies-based libraries Several small antibody fragments such as; scFv (variable light and heavy chain fragments joined by polypeptide linker), Fab (antigen binding region) have been used to prepare phage libraries. These antibody-based libraries are widely used for epitope mapping, by biopanning of the antigen or the whole cell [5]. These libraries can naive that is, they are generated by extracting antibodies antigen-immunized animals. Whereas, nonimmunized libraries are constructed by rearrangement of antibody fragment, extracted from the healthy B cells. The process is achieved by the means soeing PCR (polymerase chain reaction) [4].    1.3 BiopanningFollowing the amplification and infection of the bacteriophage viruses in the bacteria, the obtained phages are used for the biopanning process. The process involves introduction of the libraries to the target (cell, antigen, receptor or other proteins) bound onto the solid surface. Unbound phages are washed and removed whereas, bound ones are eluted, and the results are analyzed by the means ELISA (enzyme linked immunosorbent assay). In order to obtained high affinity and specific phages, 4-5 rounds of panning are performed using the phages obtained from the preceding rounds [6].This review is designed to highlight some of the significant applications of phage display in the field of medical sciences, implemented as a tool for diagnostic and therapeutic medicine.

Programmed to retain active responsivity to environmental stimuli, diverse types of synthetic gels have been attracting interests regarding various applications, such as versatile elastic biodevices. In a different approach, when the gels are made of tissue-derived biopolymers, they can act as an artificial extracellular matrix (ECM) for use as soft implants in regenerative medicine. To explore the physical properties of hydrogels in terms of statistical thermodynamics, the mean-field Flory-Huggins-Rehner theory has long been used with various analytical and numerical modifications. Here we suggest a novel mathematical model on the volume phase transition of a biological hybrid gel that is sensitive to ambient temperature. To mimic acellular soft tissues, the ECM-like hydrogel is modeled as a network of biopolymer chains, such as type I collagen and gelatin, which are covalently crosslinked and swollen in aqueous solvents. Within the network, thermoresponsive synthetic polymer chains are doped by chemical conjugation. Based on the Flory-Huggins-Rehner framework, our model phenomenologically illustrates a well-characterized volume phase behavior of engineered tissue mimics as a function of temperature by formulating the ternary mixing free energy of the polymer-solvent system and by generalizing the elastic free energy term. With this formalism, the decoupling of the Flory-Huggins interaction parameter between the thermoresponsive polymer and ECM biopolymer enables deriving a simple analytical equation for the volume phase transition as a function of the structural and compositional parameters. We show that the doping ratio of the thermoresponsive polymers affects the phase transition temperature of the ECM-like gels.

Erosion and sedimentation has a serious problem over the year especially in semi arid where soil is loose and in addition torrential rainfall. The need to develop a specissessment of rainfall induced soil erosion and sediment yield model is necessary.. Data was collected between 2018&2019 which was used to develop a dimensionless model for predicting Rainfall-induced erosion using the dimensional analyses approach. Factors used include; Soil infiltration rate, Soil erodibility factor, Hydraulic shear stress, Soil grain diameter, Depth of tilt Mean diameter of raindrop, Rainfall intensity, Rainfall duration, Gully size, and Density of soil Runoff velocity.The model produced reasonable predictions relative to field measurements with coefficient of determination R²of 0.768, the variables in the model are easily measurable; this makes it better and easily adoptable. It is recommended to use locally developed model using specific local data.

The present work aims to investigate the effect of strain reversal during High Pressure Torsion (HPT) on the evolution of microstructure and hardness properties of Aluminium-Magnesium (Al-2.5%Mg) alloy. For this purpose, Al-2.5%Mg alloy was subjected to monotonically (CW) and strain reversal (CW-CCW) deformation by High Pressure Torsion (HPT). The samples were subjected to a series of rotations in monotonically and strain reversal deformation with same equivalent strains of 1, 4, 12, 24 and 60 under an applied load of 6 GPa and with 1 rpm under quasi-constrained conditions. It was observed that Al-2.5%Mg when subjected to different routes, follows same trend in the evolution of the ultrafine structure, i.e. initial recrystallized microstructure with large grain size throughout the disk, at low strain level sub grains with prominent LAGBs network inside the grains and ultimately at the higher strains ultrafine microstructure throughout the disk characterized by equiaxed grains separated by HAGBs. The only exception to this was observed in case of Al-2.5%Mg during high strains at the centre regions where the fraction of HAGBs was found strikingly less as compared to its counterpart during strain reversal deformation. Hardness homogeneity was not observed for Al-2.5%Mg where the hardness at the centre regions was observed to be lesser than the edge regions with exceptionally less hardness at centre for strain reversal specimens at higher strains.

As digitilisation is being applied in redefining products and business models world-wide, evidence abound in the construction industry as a sector that is slow to its adoption. While digitilisation tools have been applied in modifying processes/procedures in the global North; a larger percentage of the sector in the global South is yet to be disrupted. For indigenous firms to join the rapid transformation wheel, this study reviews the interrelationship between digitilisation and building information modeling. The study objectives are to examine the prevalence of cultural and strategic capability, evaluate the relationship between cultural orientation and strategic capability as well as predict a model of building information adoption from culture and strategy. The study population was drawn from the list of construction firms registered with the Lagos State Tender board, list of registered construction firms from the Institute and specific listed firms on the internet. Factor Analysis, Correlation and Regression were the adopted statistical tools. The results revealed production; task and goal attainment; information/communication technology; workforce; innovation, learning and knowledge management as well as conflict and dispute resolution as the prevalent cultural orientations. The availability of resources to communicate, interact and collaborate digitally and leadership capability to organise and coordinate digitally are the top two strategic capabilities. Consequently, 3 out of every 5 firms have moderate awareness on BIM implementation. It was concluded that the level of agreement on the adoption of the culture and the strategy did not reflect on the level of BIM adoption model. Since the results revealed that the existing orientation and strategy contribute about a tenth of BIM adoption model; the firms’ leadership need cultural re-orientation from the client angle and from business environment. On strategy, the firms need support from institutions/government on policies that will cushion the effect of the provision of resources for transformation.

Here the interaction of three aptamers with HIV-1 protease has been investigated with the help of molecular dynamics simulations. These simulations lead to precise structural and energetic results. The sequencing of the considered aptamers is AP1 as the aptamer number 1: (CUUCAUUGUAACUUCUCAUAAUUUCCCGAGGCUUUUACUUUCGGGGUCCU), AP2 as the aptamer number 2: (CCGGGUCGUCCCCUACGGGGACUAAAGACUGUGUCCAACCGCCCUCGCCU) and AP3 as the aptamer number 3: (C, U, A, C, and C nucleotides of AP1 were replaced with A, G, G, A, and C to yield AP3). The results of molecular dynamics simulations show that aptamers 2 and 3 are good alternatives to interact with the protease enzyme and to control this enzyme, but in AP2 has somewhat improved the results. The results of MM-PBSA show that although aptamer three as a mutant aptamer has a good affinity with the protease enzyme compared to aptamer one and by impairing dimerization, it disrupts its structural stability and function. However, the results indicate that aptamer 2 is a better inhibitor because it causes a more severe conformational change in the structure of the enzyme.

1 IntroductionThe narrowing (commonly called stenosis) of blood vessels alter the regular flow of blood, being one of the most common places where these situations occur in the coronary arteries. When this situation occurs, not enough oxygen reaches the myocardium, leading to ischemic heart disease (stable or unstable angina pectoris, acute myocardial infarction). This disease is caused by sclerosis of the coronary arteries due to the formation of collagen and accumulation of lipids and inflammatory cells.In 1996, (Pijls et al., 1996) determined that there is a direct relationship between blood pressure and flow with maximum vasodilation of the artery (conditions of hyperemia). They defined the Fractional Flow Reserve (FFR), currently used as the gold standard to assess the physiological severity of coronary stenosis, as:FFR = Qms/Qmebeing:Qms: maximum achievable blood flow through a stenosis, conditions of hyperemia.Qme: maximum expected blood flow, without stenosis in the artery.The flow rate is the ratio of the pressure difference to the flow resistance:Qms = (distal diastolic pressure - venous pressure)/maximum resistance vessel stenosis.Qme = (aortic diastolic pressure - venous pressure)/maximum resistance vessel normal.\begin{equation} FFR=\frac{\left(P_{d}-P_{v}\right)/R_{s}}{\left(P_{a}-P_{v}\right)/R_{n}}\nonumber \\ \end{equation}The venous pressure (Pv) is the same and the resistances (Rs, Rn) in hyperemia are minimal, so it has that Fractional Flow Reserve is the ratio between the pressures (average of the cardiac cycle) distal coronary (Pd) and proximal or aortic (Pa) with respect to the stenosis, in conditions of hyperemia:FFR = Pd/PaThis is an invasive test, needing to insert a catheter through the coronary stenosis. The standardized medical protocol (Coppel et al., 2019) suggests measuring the distal coronary pressure (Pd) 2-3 cm downstream of the stenosis. They determined that a cut-off value of 0.75 Fractional Flow Reserve could be correctly determined for patients with ischemia, with 93% accuracy. It is currently considered that, under normal flow conditions, the Fractional Flow Reserve value should be in a range between 0.8 and 1 (Toth et al., 2016). Myocardial ischemia is highly possible when this value is below 0.8. The disadvantage of this process is that it limits the region where the pressure is measured without taking into account the evolution of the pressure field downstream of the stenosis.Since to obtain the distal and aortic pressures it is necessary to perform an invasive test, a possible substitute could be simulating the sanguineous flow in a virtual model using Computational Fluid Dynamics (CFD). This three-dimensional model can obtain from images (Min et al., 2011; Zhang et al., 2018; Owida et al., 2012) of a Coronary Computed Tomography Angiography (CCTA). To obtain clear images of the arteries that supply blood to the heart, an injection of contrast material with iodine is used. This process, known as Fractional Flow Reserve - Computed Tomography (FFRCT), allows visualizing inside the flow all type of variables and, consequently, the distribution of Fractional Flow Reserve in the stenosed artery.The main objective of this study is to deepen this Fractional Flow Reserve - Computed Tomography (FFRCT) technique examining the influence of the location of the measurement point distal coronary pressure (Pd) in the FFRCTvalue. For this purpose, a three-dimensional model was obtained from a Coronary Computed Tomography Angiography of an anonymous patient with coronary stenosis (68%) and simulated using Computational Fluid Dynamics. The results were validated with the data of distal and proximal pressures, acquired simultaneously to the same person.

INTRODUCTION Propagating fronts are characteristic for many physical phenomena. In case of reaction-diffusion-advection processes, these can be combustion or strain fronts. Solutions having large gradients to problems of this type also arise in nonlinear acoustics. Such problems include, for example, the Burgers equation, as well as equations with modular nonlinearity. The stationary reaction-diffusion-advection equations can be used for modelling of wind field distribution in the presence of plant heterogeneity. The domain where the solution has a large gradient is called the internal transition layer. The numerical implementation of solutions to problems with internal transition layers requires a preliminary analysis of the existence conditions and stability. In particular, for the numerical solution of some applied problems, the calculation method for establishing is often used, when the solution of the boundary value problem for the elliptic equation is found numerically as the solution of the corresponding initial-boundary value problem for the parabolic equation over a sufficiently long period of time. To implement this method, information on the asymptotic stability and the domain of attraction of the stationary solution is needed. In this paper, we consider the initial-boundary-value problem for reaction-diffusion-advection equation and the question of its moving front type solution stabilizing over an infinitely large time interval to the solution of the corresponding stationary problem. The existence of moving front solution is investigated in. The existence conditions of an asymptotically stable solution to the stationary problem are known from. To prove the stabilization theorem, in this paper we use the method of upper and lower solutions, which for this class of problems is justified in. The main idea of the proof is to show that the upper and lower solutions of the initial-boundary-value problem on an asymptotically large time interval fall into the attraction domain of the stationary solution. The upper and lower solutions with large gradients in the region of the internal transition layer are constructed according to the asymptotic method of differential inequalities as modifications of asymptotic approximations of the solutions to these problems in a small parameter. A small parameter here is the width of the inner transition layer with respect to the width of the front propagation region. The study conducted in this work gives an answer about non-local domain of attraction of the stationary solution. In addition, an estimate of the time interval is obtained in which the solution of the front type falls into the local domain of attraction of the stationary solution, that is, in fact, the criterion for the numerical solution stationing.

We introduce a neural field equation with a neuron-dependent Heaviside-type activation function and spatial-dependent delay. The basic object of the study is represented by a Volterra Hammerstein integral equation involving a discontinuous nonlinearity with respect to the state variable that is both time- and space-dependent. We replace the discontinuous nonlinearity by its multi-valued convexification and obtain the corresponding Volterra Hammerstein integral inclusion. We investigate the solvability of this inclusion using the properties of upper semi-continuous multi-valued mappings with convex closed values. Based on these results, we study the solvability of an initial-prehistory problem for the former neural field equation with the Heaviside-type activation function. The application of multi-valued analysis techniques allowed us to avoid some restrictive assumptions standardly used in the investigations of the solutions to neural field equations involving Heaviside-type activation functions.

In this article, the truncated exponential-Gould-Hopper polynomials are taken as base with the Appell polynomials to introduce a hybrid family of truncated exponential-Gould-Hopper-Appell polynomials. These polynomials are framed within the context of monomiality principle and their determinant definition and properties are established. Further, we investigate some members belonging to this family. In addition graphical representation and zeros of these members are demonstrated using computer experiment.

We consider three different diffusion processes in a system with a thin membrane: normal diffusion, classical subdiffusion, and slow subdiffusion. We conduct the considerations following the rule: {\it If a diffusion equation is derived from a certain theoretical model, boundary conditions at a thin membrane should also be derived from this model with additional assumptions taking into account selective properties of the membrane}. To derive diffusion equations and boundary conditions at a thin membrane, we use a particle random walk model in one-dimensional membrane system in which space and time variables are discrete. Then we move from discrete to continuous variables. We show that the boundary conditions depend on both selective properties of the membrane and a type of diffusion in the system.

The Neumann boundary value problem (BVP) for the second order “stationary heat transfer” elliptic partial differential equation with variable coefficient is considered in two-dimensional bounded domain. Using an appropriate parametrix (Levi function) and applying the two-operator approach, this problem is reduced to some systems of boundary-domain integral equations (BDIEs). The two-operator BDIEs in 2D have special consideration due to their different equivalence properties as compared to higher dimensional case due to the logarithmic term in the parametrix for the associated partial differential equation. Consequently, we need to set conditions on the domain or function spaces to insure the invertibility of the corresponding layer potentials, and hence the unique solvability of BDIEs. Equivalence of the two operator BDIE systems to the original Neumann BVP, BDIEs solvability, uniqueness/non uniqueness of the solution, as well as Fredholm property and invertibility of the BDIE operator are analysed. Moreover, the two operator boundary domain integral operators for the Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators.\\ \noindent\textbf{Key words:} Partial differential equation, Two-operator Boundary-Domain Integral Equations, finite-dimensional perturbations , equivalence, invertibility.