‎‎‎‎‎‎Let $‎\mathbb{Z}_m$ be the ring of integers modulo $m$ in which $m=2^n$ for arbitrary $n$‎. ‎In this paper‎, ‎we will obtain a relationship between $wt_L(x)‎, ‎wt_L(y)$ and $wt_L(x+y)$ for any $x‎, ‎y \in ‎\mathbb{Z}_m$‎. ‎‎Let ‎$‎‎d_r^L(C)$‎‎ ‎denote ‎the ‎‎$r‎‎$‎-th generalized LEE weight for code $C$ in which ‎$‎‎C$ ‎is ‎a linear code of length $n$ over $‎\mathbb{Z}_4$‎. Also, ‎suppose that $C_1$ and $ C_2$ are two codes over $‎\mathbb{Z}_4$ and $C$ denotes the $(u‎, ‎u+v)$-construction of them‎. ‎In this paper‎, we will obtain an upper bound for $d_r^L(C)$ for all $r$‎, ‎$1 \leq r \leq rank(C)$‎. In addition, ‎we will obtain $d_1^L(C)$ in terms of $d_1^L(C_1)$ and $d_1^L(C_2)$.

The Zagros Mountains, oriented from northwest to southeast, are barriers against western winds. This study was conducted to find a mechanism for describing specific type of cyclogenesis occurrence in the Zagros LEEward. Therefore, by examining six cycles in this category, it became clear that as the cycle approaches the Zagros domains, there is an interaction between the cyclogenesis system and the Zagros Mountains, which leads to the formation of a particular thermal structure. Thus, a high pressure center is formed in the Zagros Mountains in the thermal winds. Such thermal abnormalities coincide with a decrease in static stability and dragging of the atmosphere and increasing relative tensile strength in the Zagros windfall. Then, perturbation potential vortices in upper levels stay on the lower perturbation potential temperature, atmosphere heat stress increased and cyclogenesis can occur in the LEEward. On the other hand, the average underlying temperature (1000-700) and upper (500-300) levels showed that the most important effect of the mountains is to alter the mean distribution of low levels of potential temperature and hence to change the baroclinic waves. In fact, the Zagros Mountains, with increased meridional gradient of the potential temperature in the lower layer of the atmosphere, cause a sharp difference acceleration between upper layer and low layer of thermal disturbances. Accordingly, the Zagros Mountains, in terms of creating changes in the tilt of in Baroclinicity waves, provide the basis for the cyclogenesis in its eastern parts. So, this kind of cyclogenesis is based on the mechanism of orographic modification of baroclinic waves.

The LEE-Carter model is a useful dynamic stochastic model representing the evolution of central mortality rates over time. This model only considers the uncertainty about the coefficient related to the mortality trend over time but not the age-dependent coefficients. This paper proposes a fuzzy extension of the LEE-Carter model that allows quantifying the uncertainty of both kinds of parameters. The variability of the time-dependent index is modeled as a stochastic fuzzy time series. Likewise, the uncertainty of the age-dependent coefficients is quantified using triangular fuzzy numbers. Considering this last hypothesis requires developing and solving a fuzzy regression model. Once the generalization of the desired fuzzy model is introduced, we will show how to fit the logarithm of the central mortality rate in Khuzestan province using by using fuzzy numbers arithmetic during the years 1401-1383 and random fuzzy forecast in the years 1402-1406.

Introduction: The affect phobia Questionnaire was designed by McCullough and et al. developed as effectiveness instrument of assessing, experiencing, expressing, and regulating emotions to enhance an individual basic capacity in relation to others and ourselves. Materials and Methods: In this study, 290 (men, women) nurses from several hospitals of Shiraz University of Medical Sciences and psychiatric patients referred to these centers in 2019-2020 were selected by available sampling method and them completed the Toronto Alexithymia and affect phobia questionnaires. Findings: Cronbach's alpha coefficient for the whole questionnaire was 0. 73. Test-retest reliability showed a correlation coefficient of 0. 79(for nurses group) after one month. Also, the correlation coefficient of this instrument with Alexithymia Questionnaire was-0. 33. Eigenvalues 4 larger factors is 1 and explains the percentage coverage of common variance between variables for these 4 factors on 5. 62% of the total variance of variables. Discussion and Conclusion: based on the research findings the questionnaire with four dimensions was introduced and named. The present study shows that the Affect Phobia Test could be used as a screening instrument prior to affect focused therapy. Extended Abstract Introduction Affect phobia expresses the concept of psychoanalytic conflict in the language of learning theory and the use of behavioral therapy techniques. Psychoanalytic therapy based on affect phobia believes that the emotional conflict and psychological pathology are rooted in the fear of affect. Accordingly, the affect phobia Questionnaire was designed by McCullough and coworkers developed as effective in assessing, experiencing, expressing, and regulating emotions to enhance an individual basic capacity in relation to others and ourselves. Materials and Methods This questionnaire consists of 20 items on seven subscales measuring different emotions and provides an overall score of affect phobia at the end. Answers are given on a five-point Likert scale. After translating the items and translating they back into English, the questionnaire of revision, correction, and retranslation and finally with the opinion of the professors of the psychology department of Shiraz Islamic Azad University, the Apparent and structure validity of this scale was approved. Also, after receiving the ethical code, permission to implement this project was obtained from Shiraz University of Medical Sciences. In this study, 290 (men, women) nurses from several hospitals of Shiraz University of Medical Sciences and psychiatric patients referred to these centers in 2019-2020 were selected by available sampling method and completed the Toronto Alexithymia and affect phobia questionnaires. Findings In determining the reliability of the questionnaire, Cronbach's alpha coefficient for the whole questionnaire was 0. 73. Test-retest reliability showed a correlation coefficient of 0. 79(for nurses group) after one month. Also, the correlation coefficient of this instrument with Alexithymia Questionnaire was-0. 33. The results of factor analysis of this tool showed that the KMO value is 0. 85 and the level of significance of Bartlett sphericity is less than 0. 001. Therefore, the implementation of factor analysis based on the correlation matrix obtained in the sample group will be acceptable. Eigenvalues 4 larger factors is 1 and explains the percentage coverage of common variance between variables for these 4 factors on 5. 62% of the total variance of variables. In this study, due to the commonality between the materials, the minimum coefficient of commonality was considered 0. 3. The results obtained in this section showed that the operating structure before rotation is completely different from the matrix of operating structure after rotation. Discussion and Conclusion although this questionnaire has been translated and used in different languages, but only in Sweden its psychometric properties have been examined. these questionnaire is affective and comprehensive than other tools made in the field of measuring the avoidance of emotions (McCullough et al., 2010). the result of varimax rotation of the factors showed that the questions are pure and uncomplicated and their factor load on the main factors is far from other factors, but based on the research findings and after several times performing factor analysis and extracting multiple factors and comparing the extracted factors with the theoretical structure of the questionnaire and the existing theoretical foundations, as well as considering the assumptions of factor analysis, it was decided to extract 4 factors. The last three criteria of the questionnaire are in the field of different aspects of self-relationship and due to the overlap and uniformity of the questions of these three criteria and the importance of issues related to their sense in mental health, the last three criteria are considered as a single criterion in relation to themselves. And a satisfactory reliability score was obtained. As a result, based on the obtained validity, the questionnaire with four dimensions was introduced and named. The present study shows that the Affect Phobia Test could be used as a screening instrument prior to affect focused therapy.

People with Parkinson's disease (PD) often have walking difficulty in the advanced stages of the disease and also suffer from balance problems. They perform their functional movements in a smaller range and at a slower rate, which will cause difficulty in performing daily activities. Patients with PD face many difficulties in outdoor activities, community participation, personal tasks, and fine motor skills (e. g. writing). They usually need the help of others. For two decades, a new treatment called LEE Silverman Voice Treatment (LSVT) has been used by the speech therapists to treat speech and swallowing disorders in PD patients based on evidence and principles of neuroplasticity. The BIG protocol was added to this method in 2010 (LSVT-BIG). In this method, the whole body is involved and its main focus is on motor skills, which are guided by a physiotherapist and occupational therapist. The main goal of this new method is to improve patient’ s skilled movement in PD, as opposed to the old methods that introduce muscle stiffness as the main problem in these patients. In this method, patients will be required to perform a series of special exercises in sitting and standing positions in a larger range than usual with a specific schedule and in a one-month intensive period. Doing the BIG protocol correctly can make the range of motion softer and larger. The studies also show that the LSVT BIG method is very effective for improving patients' walking patterns and daily activities and significantly increases the quality of life in PD patients. Eventually, the PD patients will be able to perform their motor tasks automatically. Considering the useful results of this method and also the growing trend of its application around the world, it is necessary to enable therapists with this new method and provide more complete services for PD patients.

In 2004, Hwang et al. proposed a group key exchange protocol for sharing a secure key in a group. Their protocol is an extension from the two party key exchange protocol to the group one. Recently, Jung-San LEE et al. noted that Hwang et al. group key exchange protocol has two security weaknesses. First, the forward secrecy is not con rmed in case that a new member joins the group and second, if a group member leaves the group, the backward secrecy is compromised. They proposed an improvement over this key exchange protocol in order to provide both forward and backward secrecy among group members. In this paper, we propose another improvement over LEE et al. key exchange, and we show that our key exchange protocol not only preservers both forward and backward secrecy, but also it is more e cient than their protocol when a member leaves the group. Finally, we give a formal analysis for the correctness of the proposed protocol via Scyther model checking tool.

Mortality Predictions can be made in two ways: First, indirect prediction through life expectancy and then conversion to age specific mortality rates, and the second is direct prediction of mortality rates. In the first approach, it is assumed that after the transition period, which is generally a higher level of life expectancy at birth of 70 years, life expectancy increments decrease and that the increase will be negligible asymptotically. In the second approach, age specific mortality rate is predicted to obtain life expectancy using the direct method of life table construction. Logically, the correct and most plausible method of estimation and to predict life expectancy is the second approach. In addition, usually the indirect method has larger odds and errors. The purpose of this paper is to use the second approach and predict mortality rates using Iranian mortality data in the LEE - Carter model for life insurance calculations. This model has two main factors: period and age. An important and difficult assumption of this model is the relative stability of age pattern of mortality. As various evaluations have shown, under these conditions error of the LEE - Carter model is less than any other method in direct predicting of mortality rates. For Iranian data, our assessments show that the estimation error is small, although this element is higher in some ages. However, hypothesis tests on the stability of the age pattern of mortality in Iran, is the subject of future research.

Introduction Due to their height, geometry and orientation, the mountains affect the atmospheric currents. Therefore, mountains cause the formation, intensification or weakening of many atmospheric phenomena. One of the most obvious of these phenomena is LEE cyclogenesis whose formation and evolution is subject to interaction between mountains and atmospheric currents. The LEE sides of mesoscale or large-scale mountains, such as the Alps, Rocky Mountains, the East Asian mountains and the Andes, are favorable regions of cyclogenesis. This type of cyclogenesis is known as LEE cyclogenesis, and can be defined as the formation of a cyclone with strong positive vertical vorticity or an appreciable fall in pressure with a closed circulation formed in the LEE of a mountain that then drifts away (Chung. et al, 1976). In this regard, most studies have been made about the LEE cyclogenesis of the Alps and the Rocky Mountains. As a result, the general understanding of mechanism of LEE cyclogenesis is derived from studies conducted on these two mountains and partially due to the Alpine Experiment (ALPEX) field project held in 1982. In other words, the general framework of the mechanisms that exists today about LEE cyclogenesis is based on the results obtained from the study of the Alps and the Rocky Mountains. Methodology The variables used in this study are consists of horizontal wind speed (u and v), vertical wind speed vertical pressure coordinates (w), temperature (T) geopotential pressure levels (z). The data variables used 1 and 0. 5 degrees in the horizontal and vertical distance of 50 hPa from 1000 to 200 hPa. The data were extracting from the archival database ECMWF ERA Interim version with six-hour monitoring. Preliminary investigations showed that unstable systems under certain elevation models are located in the middle of the atmosphere in the region of the west, northwest of the west and west to the upstream slopes of the Zagros Mountains. so that the study of middle-level maps showed how the trough and the ridge of such systems has played an important role in determining the direction and movement of these systems towards zagros because it is different in terms of the confluence or diffluence system, curvature and sheer vorticity advection and ageostrophic wind of the trough, and finally the direction in the trough. In general, the conditions prevailing on these systems and the it direction they pass through to the Zagros have an important role in how they interact with the zagros. Therefore, it is necessary to examine how these systems approach to Zagros. For this purpose, this important issue was further investigated using the ageostrophic wind equation. Because the ageostrophic wind indicates the imbalance of geostrophic, and in fact the change of wind both in space and time causes this imbalance of geostrophic and the creation of the ageostrophic wind (Lynch and Cassano 2006, 123). Also used curvature vorticity in the natural coordinates, quasi-geostrophic height tendency equation and divergence of the isallobaric wind. Results and discussion An examination of the maps of the lower atmospheric levels shows that in some cases the cyclones approaching the windward slopes of the Zagros, under the baroclinic wave’ s atmosphere, lead to the formation of a secondary rotation in the LEE ward Zagros. Therefore, it is necessary to have a primary cyclone on the windward slope of the Zagros Mountains to form the LEE cyclone. So the detection of cyclone approaching windward of the Zagros Mountains shows that cyclones which move and even higher than the Mediterranean latitude to the east, would have approached the Zagros in a way that was accompanied by a pattern of confluence ridge-diffluence trough in the middle of the atmosphere. While the cyclones, accompanied by a trough, were moving northward along the path of their eastward before reaching the Zagros in the north east. On the other hand, the cyclons, formed in the Red Sea region or Sudan, were required to reach the Zagros Mountains (the maximum velocity at the base of the trough) or the diffluence trough to approach the zagros. At the same time, the cyclones that were located in the area were under a confluence trough, never moved to the Zagros Mountains. So, according to the latitude of the primary cyclone and how the stack-trough is the level of 500 hpa, the path of the approaching Zagros is different. However, in many cases the nature of the trough and the level of the level of 500 hpa on the path of the eastward movement changes from difflunce to confluence and vice versa, which occurs due to the changing location in the baroclinic wave. Conclusion Because The Zagros Mountains create changes in approaching baroclinicity waves causes advent thermal anomaly and consequently cause the occurrence of cyclone, so, such cyclogenesis is interpreted adjust according to the theory modify baroclinicity waves. Because this theory clearly states that mountain lead to LEE cyclogenesis by modify baroclinicity. It is worth noting that many of the much complexities of the relationship between the Zagros Mountains and baroclinicity waves that may cause the occurrence of cyclones are a variety of other theories proposed in the literature to be more consistent Atmospheric Sciences. In any case, this study is based on small portions and a special kind of cyclogenesis can be in the Zagros LEEward.