990 research outputs found
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 is called a generalized
\unicode{x00A3}-cotosion group if contains an open
\unicode{x00A3}-cotosion subgroup such that 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 form a topology
on which is denoted by . We investigate the relations between
topological properties of with the topology and . Also, we
introduce the concept of a continuous map
HÀgusad teist liiki integraalvÔrrandid
KÀesolevas doktoritöös on uuritud hÀgusaid teist liiki integraalvÔrrandeid. Need vÔrrandid sisaldavad hÀgusaid funktsioone, s.t. funktsioone, mille vÀÀrtused on hÀgusad arvud.
Me tĂ”estasime tulemuse sileda tuumaga hĂ€gusate Volterra integraalvĂ”rrandite lahendite sileduse kohta. Kui integraalvĂ”rrandi tuum muudab mĂ€rki, siis integraalvĂ”rrandi lahend pole ĂŒldiselt sile. Nende vĂ”rrandite lahendamiseks me vaatlesime kollokatsioonimeetodit tĂŒkiti lineaarsete ja tĂŒkiti konstantsete funktsioonide ruumis. Kasutades lahendi sileduse tulemusi tĂ”estasime meetodite koonduvuskiiruse.
Me vaatlesime ka nĂ”rgalt singulaarse tuumaga hĂ€gusaid Volterra integraalvĂ”rrandeid. Uurisime lahendi olemasolu, ĂŒhesust, siledust ja hĂ€gusust. Ălesande ligikaudseks lahendamiseks kasutasime kollokatsioonimeetodit tĂŒkiti polĂŒnoomide ruumis. TĂ”estasime meetodite koonduvuskiiruse ning uurisime lĂ€hislahendi hĂ€gusust. Nii analĂŒĂŒs kui ka numbrilised eksperimendid nĂ€itavad, et gradueeritud vĂ”rke kasutades saame parema koonduvuskiiruse kui ĂŒhtlase vĂ”rgu korral.
Teist liiki hĂ€gusate Fredholmi integraalvĂ”rrandite lahendamiseks pakkusime uue lahendusmeetodi, mis pĂ”hineb kĂ”igi vĂ”rrandis esinevate funktsioonide lĂ€hendamisel TĆĄebÔƥovi polĂŒnoomidega. Uurisime nii tĂ€pse kui ka ligikaudse lahendi olemasolu ja ĂŒhesust. TĂ”estasime meetodi koonduvuse ja lĂ€hislahendi hĂ€gususe.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
On TFU extensions in LCA groups
Let be the category of all locally compact abelian (LCA) groups. Let
and . The first Ulm subgroup of is denoted by
and the closure of by . A proper short exact
sequence in is
said to be a extension if is a
proper short exact sequence where
and
. We introduce some results on
extensions. Also, we establish conditions under which the
extensions split
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
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