S-pure Extensions of Locally Compact Abelian Groups

In this paper, we introduce the concept and study some properties of an s-pure subgroup and a s-pure extension in the category of locally compact abelian groups.Comment: 11 pages, accepted for publications in Hacettepe Journal of Mathematics and Statistic

On T-locally compact spaces

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact. T-locally compact is a topological property. T-locally compact is not preserved by the product topology

On generalized \unicode{x00A3}-cotorsion LCA groups

A locally compact abelian group $G$ is called a generalized \unicode{x00A3}-cotosion group if $G$ contains an open \unicode{x00A3}-cotosion subgroup $H$ such that $G/H$ is a cotorsion group. In this paper, we determine the generalized \unicode{x00A3}-cotorsion LCA groups

∗−*-open sets and ∗−*- continuity in topological spaces

In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between topological properties of $X$ with the topology $^{*}O(X)$ and $X$. Also, we introduce the concept of a $*-$continuous map

Hägusad teist liiki integraalvõrrandid

Käesolevas doktoritöös on uuritud hägusaid teist liiki integraalvõrrandeid. Need võrrandid sisaldavad hägusaid funktsioone, s.t. funktsioone, mille väärtused on hägusad arvud. Me tõestasime tulemuse sileda tuumaga hägusate Volterra integraalvõrrandite lahendite sileduse kohta. Kui integraalvõrrandi tuum muudab märki, siis integraalvõrrandi lahend pole üldiselt sile. Nende võrrandite lahendamiseks me vaatlesime kollokatsioonimeetodit tükiti lineaarsete ja tükiti konstantsete funktsioonide ruumis. Kasutades lahendi sileduse tulemusi tõestasime meetodite koonduvuskiiruse. Me vaatlesime ka nõrgalt singulaarse tuumaga hägusaid Volterra integraalvõrrandeid. Uurisime lahendi olemasolu, ühesust, siledust ja hägusust. Ülesande ligikaudseks lahendamiseks kasutasime kollokatsioonimeetodit tükiti polünoomide ruumis. Tõestasime meetodite koonduvuskiiruse ning uurisime lähislahendi hägusust. Nii analüüs kui ka numbrilised eksperimendid näitavad, et gradueeritud võrke kasutades saame parema koonduvuskiiruse kui ühtlase võrgu korral. Teist liiki hägusate Fredholmi integraalvõrrandite lahendamiseks pakkusime uue lahendusmeetodi, mis põhineb kõigi võrrandis esinevate funktsioonide lähendamisel Tšebõšovi polünoomidega. Uurisime nii täpse kui ka ligikaudse lahendi olemasolu ja ühesust. Tõestasime meetodi koonduvuse ja lähislahendi hägususe.In this thesis we investigated fuzzy integral equations of the second kind. These equations contain fuzzy functions, i.e. functions whose values are fuzzy numbers. We proved a regularity result for solution of fuzzy Volterra integral equations with smooth kernels. If the kernel changes sign, then the solution is not smooth in general. We proposed collocation method with triangular and rectangular basis functions for solving these equations. Using the regularity result we estimated the order of convergence of these methods. We also investigated fuzzy Volterra integral equations with weakly singular kernels. The existence, regularity and the fuzziness of the exact solution is studied. Collocation methods on discontinuous piecewise polynomial spaces are proposed. A convergence analysis is given. The fuzziness of the approximate solution is investigated. Both the analysis and numerical methods show that graded mesh is better than uniform mesh for these problems. We proposed a new numerical method for solving fuzzy Fredholm integral equations of the second kind. This method is based on approximation of all functions involved by Chebyshev polynomials. We analyzed the existence and uniqueness of both exact and approximate fuzzy solutions. We proved the convergence and fuzziness of the approximate solution.https://www.ester.ee/record=b539569

Effect of mental training on short-term psychomotor skill acquisition in laparoscopic surgery - a pilot study

Aim: The mental demands of laparoscopic surgery create a steep learning curve for surgical trainees. Experienced surgeons informally conduct mental training prior to starting a complex laparoscopic procedure. Reconstructing haptic feedback to mentally observe surgeon-instrument-tissue interaction is considered to be acquired only with experience. An experiment was devised to implement mental training for the haptic feedback reconstruction and its effect on laparoscopic task performance was observed.Methods: Twenty laparoscopy novice medical students with normal/corrected visual acuity and normal hearing were randomised into two groups. Both groups were asked to apply a pre-established consistent force by means of retracting a laparoscopic grasper fixed to an electronic weight scale. Studied group underwent mental training while control group conducted a laparoscopic task as a distraction exercise. Accuracy of the task performance was measured as primary outcome. Performance between dominant and non-dominant hands was the secondary outcome.Results: Baseline assessment of both dominant and non-dominant hands between groups were similar (P > 0.05). Mental training group improved their performance (0.66 ± 0.04) vs. (1.06 ± 0.14) with dominant hand (P < 0.01) and (0.73 ± 0.04) vs. (1.10 ± 0.20) with non-dominant hand (P < 0.05), when compared with control group.Conclusion: In a laparoscopic task performance, skill transfer is significantly accurate if mental haptic feedback reconstruction is achieved through mental training

Fractional Concepts in Neural Networks: Enhancing Activation and Loss Functions

The paper presents a method for using fractional concepts in a neural network to modify the activation and loss functions. The methodology allows the neural network to define and optimize its activation functions by determining the fractional derivative order of the training process as an additional hyperparameter. This will enable neurons in the network to adjust their activation functions to match input data better and reduce output errors, potentially improving the network's overall performance.Comment: 12 pages, 6 figures, submitted to Neurocomputing journa

Analysis of climate hazards in relation to urban designing in Iran

In order to study the climate hazards, daily rainfall and temperature data of 61 weather stations over the country were obtained from the Meteorological Organization of Iran for the 1951–2007 period. The following indices are defined as indications of climate hazards: sultriness of the air or the heat index, cold days with minimum temperature below −5 °C, warm days with maximum temperature above 32 °C, the share of extreme rain days from the annual rainfall. The annual frequencies of these indices are analyzed and the overall hazard index is computed using the Analytical Hierarchical Process method. The results show that the southern coastal areas and central deserts are the most hazardous parts of the country, whereas, the northern Caspian coastal lands and mountainous regions experience lower hazard alerts. The problem of the northern parts is the cold days and that of the southern areas is the hot and humid days. Despite the relatively equal occurrence of torrential rains over the country, they are more harmful in the south than in the other parts of the country

On t-extensions of abelian groups

Let G and C be two discrete abelian groups. It is known that Pext(C,G) is a subgroup of Ext(C,G). In this paper, we introduce the t-extensions of G by C. We will show that the set of all t-extensions of G by C is a subgroup of Ext(C,G) which contains Pext(C,G). Fulp and Griffith [4] determined the LCA groups G such that Ext(C,G)=0 for all compact connected groups C. Using the group of t-extensions, we determine the LCA groups G such that Pext(C,G)=0 for all compact connected groups C