Search results for: physiological functions

Authors: Fuad Al Sarari

Abstract:

The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.

Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions

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Authors: Naveed Tahir, Adnan Maqsood

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Cognitive workload is a significant factor affecting user performance, and it has been broadly investigated for its application in ergonomics as well as in designing and optimizing effective human-machine interactions. It is mentally challenging to maneuver an aircraft, and pilots must control the aircraft and adequately communicate to the verbal-auditory stimuli. Several physiological measures have long been researched and used to demonstrate the cognitive workload. In our current study, we have summarized recent findings of the effectiveness, accuracy, and applicability of commonly used physiological measures in evaluating cognitive workload. We have also highlighted on the advancements in physiological measures. The strength and limitations of physiological measures have also been discussed to assess the cognitive workload of people, especially the aircrews in laboratory settings and real-time situations. We have presented the research findings of the physiological measures to base suggestions on the proper applications of the measures and settings demanding the use of single measure or their combinations.

Keywords: aircrew, cognitive workload, subjective measure, physiological measure, performance measure

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Authors: Ilango Thiagalingam, Erwann Yvin, Gabriel Crehan, Roch El Khoury

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An experimental investigation is carried out in order to evaluate the relevance of a customization approach of the passive thermal mannikin. The promise of this approach consists in the following assumption: physiological differences lead to distinct thermo-physiological responses that explain a part of the thermal appraisal differences between people. Categorizing people and developing an appropriate thermal mannikin for each group would help to reduce the actual dispersion on the subjective thermal comfort perception. The present investigation indicates that popular passive physiological diversity drivers such as sex, age and BMI are not the correct parameters to consider. Indeed, very little or no discriminated global thermo-physiological responses arise from the physiological classification of the population using these parameters.

Keywords: thermal comfort, thermo-physiology, customization, thermal mannikin

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Authors: Abdesselam Babouri, Ahcène Lemzadmi, M Rahmane, B. Belhadi, N. Abouchi

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Medical monitoring aims at monitoring and remotely controlling the vital physiological parameters of the patient. The physiological sensors provide repetitive measurements of these parameters in the form of electrical signals that vary continuously over time. Various measures allow informing us about the health of the person's physiological data (weight, blood pressure, heart rate or specific to a disease), environmental conditions (temperature, humidity, light, noise level) and displacement and movements (physical efforts and the completion of major daily living activities). The collected data will allow monitoring the patient’s condition and alerting in case of modification. They are also used in the diagnosis and decision making on medical treatment and the health of the patient. This work presents the implementation of a monitoring system to be used for the control of physiological parameters.

Keywords: clinical monitoring, physiological parameters, biomedical sensors, personal health

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Authors: Muna Tabuni

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The paper contains an investigation of the behavior of the Zeros of Bargmann functions for one and two-mode systems. A brief introduction to Harmonic oscillator formalism for one and two-mode is given. The Bargmann analytic representation for one and two-mode has been studied. The zeros of Bargmann analytic function for one-mode are considered. The Q Husimi functions are introduced. The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros are discussed. The zeros of Bargmann analytic functions for two-mode are introduced. Various examples have been given.

Keywords: Bargmann functions, two-mode, zeros, harmonic oscillator

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Masaki Omata, Shumma Hosokawa

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An experiment to verify the relationships between physiological indexes of an e-learner and the presence or absence of an operation during e-learning is described. Electroencephalogram (EEG), hemoencephalography (HEG), skin conductance (SC), and blood volume pulse (BVP) values were measured while participants performed experimental learning tasks. The results show that there are significant differences between the SC values when reading with clicking on learning materials and the SC values when reading without clicking, and between the HEG ratio when reading (with and without clicking) and the HEG ratio when resting for four of five participants. We conclude that the SC signals can be used to estimate whether or not a learner is performing an active task and that the HEG ratios can be used to estimate whether a learner is learning.

Keywords: e-learning, physiological index, physiological signal, state of learning

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Authors: Alicia C. Sanchez

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This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.

Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation

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Authors: Fatemeh Deldarabdolmaleki, Nur Dalilah Dahlan, Farzad Hejazi

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Human individual physiological and psycho-physical responses widely affect thermal comfort and preferences. They should be carefully researched to help improve the design and comfort of indoor environments. This paper aims to explore and test the degree and importance of individual physiological and psycho-physical differences, reviewing the most preferred, neutral, and comfortable temperature in previous studies conducted across the world. Basic individual physiological differences like gender, age, BMI and etc., have been the focus of this research. There is no unique consensus in the literature to date in regard to providing a universal thermal comfort formula that meets all individual physiological and psycho-physical needs. In order to achieve a balanced, thermally comfortable indoor environment, studying and evaluating individual needs in different parts of the world could be helpful. Even though personalized comfort systems in indoor environments sound promising, they might not be easily achieved in bigger office interiors, considering the cost and current open-plan office trends.

Keywords: thermal comfort, indoor environments, occupants' physiological response, occupants psycho-physical response

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Mehmet Karahan, Nevin Karahan

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Water and air permeability and thermal resistance of fabrics are the important attributes which strongly influence the thermo-physiological comfort properties of sportswear fabrics in different environmental conditions. In this work, terry and fleece fabrics were developed by varying the fiber content and areal density of fabrics. Further, the thermo-physical properties, including air permeability, water vapor permeability, and thermal resistance, of the developed fabrics were analyzed before and after washing. The multi-response optimization of thermo-physiological comfort properties was done by using principal component analysis (PCA) and Taguchi signal to noise ratio (PCA-S/N ratio) for optimal properties. It was found that the selected parameters resulted in a significant effect on thermo-physiological comfort properties of knitted fabrics. The PCA analysis showed that before wash, 100% cotton fabric with an aerial weight of 220 g.m⁻² gave optimum values of thermo-physiological comfort.

Keywords: thermo-physiological comfort, fleece knitted fabric, air permeability, water vapor transmission, cotton/polyester

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Authors: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Larisa Gheber

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Mitosis is an essential process by which duplicated genetic information is transmitted from mother to daughter cells. Incorrect chromosome segregation during mitosis can lead to genetic diseases, chromosome instability and cancer. This process is mediated by a dynamic microtubule-based intracellular structure, the mitotic spindle. One of the major factors that govern the mitotic spindle dynamics are the kinesin-5 biological nano motors that were believed to move unidirectionally on the microtubule filaments, using ATP hydrolysis, thus performing essential functions in mitotic spindle dynamics. Surprisingly, several reports from our and other laboratories have demonstrated that some kinesin-5 motors are bi-directional: they move in minus-end direction on the microtubules as single-molecules and can switch directionality under a number of conditions. These findings broke a twenty-five-years old dogma regarding kinesin directionality (1, 2). The mechanism of this bi-directional motility and its physiological significance remain unclear. To address this unresolved problem, we apply an interdisciplinary approach combining live cell imaging, biophysical single molecule, and structural experiments to examine the activity of these motors and their mutated variants in vivo and in vitro. Our data shows that factors such as protein phosphorylation (3, 4), motor clustering on the microtubules (5, 6) and structural elements (7, 8) regulate the bi-directional motility of kinesin motors. We also show, using Cryo-EM, that bi-directional kinesin motors obtain non-canonical microtubule binding, which is essential to their special motile properties and intracellular functions. We will discuss the implication of these findings to mechanism bi-directional motility and physiological roles in mitosis.

Keywords: mitosis, cancer, kinesin, microtubules, biochemistry, biophysics

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Authors: Radwa E. Sweif, Amira A. A. Abdallah

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Background: Evaluation of gait efficiency is used to examine energy consumption especially in patients with movement disorders. Hypothesis/Purpose: This study compared the physiological and mechanical measures of gait efficiency between patients with ACL reconstruction (ACLR) and healthy controls and correlated among these measures. Methods: Seventeen patients with ACLR and sixteen healthy controls with mean ± SD age 23.06±4.76 vs 24.85±6.47 years, height 173.93±6.54 vs 175.64±7.37cm, and weight 74.25±12.1 vs 76.52±10.14 kg, respectively, participated in the study. The patients were operated on six months prior to testing. They should have completed their accelerated rehabilitation program during this period. A 3D motion analysis system was used for collecting the mechanical measures (Biomechanical Efficiency Quotient (BEQ), the maximum degree of knee internal rotation during stance phase and speed of walking). The physiological measures (Physiological Cost Index (PCI) and Rate of Perceived Exertion (RPE)) were collected after performing the 6- minute walking test. Results: MANOVA showed that the maximum degree of knee internal rotation, PCI, and RPE increased and the speed decreased significantly (p<0.05) in the patients compared with the controls with no significant difference for the BEQ. Finally, there were significant (p<0.05) positive correlations between each of the PCI & RPE and each of the BEQ, speed of walking and the maximum degree of knee internal rotation in each group. Conclusion: It was concluded that there are alterations in both mechanical and physiological measures of gait efficiency in patients with ACLR after being rehabilitated, clarifying the need for performing additional endurance as well as knee stability training programs. Moreover, the positive correlations indicate that using either of the mechanical or physiological measures for evaluating gait efficiency is acceptable.

Keywords: ACL reconstruction, mechanical, physiological, gait efficiency

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Mohammad Salameh Almasarweh

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The primary aim of this research is to explore the mediating role of physiological climate in the relationship between green HRM practices (specifically, GHRM practices, GHRM recruitment, GHRM training, GHRM performance appraisal, and GHRM empowerment) and employee performance within the hotel industry. The study revealed that green HRM practices, encompassing green recruiting, green training, green performance evaluation, and green empowerment, exerted a statistically significant influence on employee performance. A quantitative method was employed for this research, focusing on hotel managers in Jordan as the study's population. Data were collected through a questionnaire distributed to a convenience sample of 300 managers from various hotels in Jordan. The results of the study align with prior research, supporting the notion that green HRM practices positively impact both employee performance and physiological climate. Furthermore, the findings of this study indicate that physiological climate acts as a mediating factor in the relationship between green HRM practices and employee performance in Jordanian hotels.

Keywords: GHRM practices, GHRM recruitment, GHRM training, GHRM performance appraisal, GHRM empowerment, employee’s performance, physiological climate

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Authors: L. Bikulciene, E. Venskaityte, G. Jarusevicius

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Non-stationary and nonlinear signals generated by living complex systems defy traditional mechanistic approaches, which are based on homeostasis. Previous our studies have shown that the evaluation of the interactions of physiological signals by using special analysis methods is suitable for observation of physiological processes. It is demonstrated the possibility of using deep physiological model, based interpretation of the changes of the human body’s functional states combined with an application of the analytical method based on matrix theory for the physiological signals analysis, which was applied on high risk cardiac patients. It is shown that evaluation of cardiac signals interactions show peculiar for each individual functional changes at the onset of hemodynamic restoration procedure. Therefore we suggest that the alterations of functional state of the body, after patients overcome surgery can be complemented by the data received from the suggested approach of the evaluation of functional variables interactions.

Keywords: cardiac diseases, complex systems theory, ECG analysis, matrix analysis

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Authors: Yousif Mohamed Y. Abdallah, Khalid H. Eltom

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This is an experimental study deals with measurement of the periodic physiological organ motion during lung external irradiation in order to reduce the exposure of healthy tissue during radiation treatments. The results showed for left lung displacement reading (4.52+1.99 mm) and right lung is (8.21+3.77 mm) which the radiotherapy physician should take suitable countermeasures in case of significant errors. The motion ranged between 2.13 mm and 12.2 mm (low and high). In conclusion, the calculation of tumour mobility can improve the accuracy of target areas definition in patients undergo Sterostatic RT for stage I, II and III lung cancer (NSCLC). Definition of the target volume based on a high resolution CT scan with a margin of 3-5 mm is appropriate.

Keywords: physiological motion, lung, external irradiation, radiation medicine

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Chiahi Nadia

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The aim of our work is to monitor the behavior of soft wheat on a morpho-physiological and agronomic scale under the influence of treated wastewater. Physico-chemical analyses of the treated sewage were also carried out, and our tests were carried out on two varieties of common wheat (Triticum aestivum L), HD1220 and ARZ. For this, a seedling was made, and two different irrigations were chosen, one using treated wastewater from the Sedrata (Wilaya of Souk ahras - Algeria) WWTP and the other stormwater as a control. The tests focused on soil and soft wheat parameters, and based on our results, the soft wheat development, physiological and yield parameters appear to respond favorably to the use of these waters.

Keywords: common wheat (Triticum aestivum L.), purified wastewater, irrigation, morph physiological and agronomic parameters

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Authors: Ammar S. M. Moohialdin, Bambang T. Suhariadi, Mohsin Siddiqui

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This paper addresses the application of physiological status monitoring (PSM) for assessing the impact of harsh weather conditions on sports activities in universities in Saudi Arabia. Real sports measurement was conducted during sports activities such that the physiological status (HR and BR) of five students were continuously monitored by using Zephyr BioHarness^TM 3.0 sensors in order to identify the physiological bonds and zones. These bonds and zones were employed as indicators of the associated physiological risks of the performed sports activities. Furthermore, a short yes/no questionnaire was applied to collect information on participants’ health conditions and opinions of the applied PSM sensors. The results show the absence of a warning system as a protective aid for the hazardous levels of extremely hot and humid weather conditions that may cause dangerous and fatal circumstances. The applied formulas for estimating maximum HR provides accurate estimations for Maximum Heart Rate (HR_max). The physiological results reveal that the performed activities by the participants are considered the highest category (90–100%) in terms of activity intensity. This category is associated with higher HR, BR and physiological risks including losing the ability to control human body behaviors. Therefore, there is a need for immediate intervention actions to reduce the intensity of the performed activities to safer zones. The outcomes of this study assist the safety improvement of sports activities inside universities and athletes performing their sports activities. To the best of our knowledge, this is the first paper to represent a special case of the application of PSM technology for assessing sports activities in universities considering the impacts of harsh weather conditions on students’ health and safety.

Keywords: physiological status monitoring (PSM), heart rate (HR), breathing rate (BR), Arabian Gulf

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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