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Yasin \"{U}nl\"{u}t\"{u}rk,S\"{u}ha Y\i lmaz,Cumali Ekici 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
A NEW MODELLING OF TIMELIKE Q-HELICES
( Yasin Ünlütürk ),( Cumali Ekici ),( Doǧan Ünal ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In this study, we mean that timelike q-helices are curves whose q-frame fields make a constant angle with a non-zero fixed axis. We present the necessary and sufficient conditions for timelike curves via the q-frame to be q-helices in Lorentz-Minkowski 3-space. Then we find some results of the relations between q-helices and Darboux q-helices. Furthermore, we portray Darboux q-helices as special curves whose Darboux vector makes a constant angle with a non-zero fixed axis by choosing the curve as one of the types of q-helices, and also the general case.
A NEW CONSTRUCTION OF TIMELIKE RULED SURFACES WITH CONSTANT DISTELI-AXIS
( Rashad A. Abdel-baky ),( Yasin Ünlütürk ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
In this study, we construct timelike ruled surfaces whose Disteli-axis is constant in Minkowski 3-space □. Then we attain a general system characterizing these surfaces, and also give necessary and sufficient conditions for a timelike ruled surface to get a constant Disteli-axis.
Mü,ge Urgu,Aylin Tü,rk,Sevcan Ü,nlü,tü,rk,Figen Kaymak-Ertekin,Nurcan Koca 한국축산식품학회 2019 한국축산식품학회지 Vol.39 No.1
Fat reduction in the formulation of cheese emulsion causes problems in its flowability and functional characteristics during spray-dried cheese powder production. In order to eliminate these problems, the potential of using microparticulated whey protein (MWP) in cheese emulsions was examined in this study. Reduced-fat whitebrined cheese emulsions (RF) with different dry-matters (DM) (15%, 20%, and 25% excluding emulsifying salt) were produced using various MWP concentrations (0%–20% based on cheese DM of emulsion). Their key characteristics were compared to full-fat cheese emulsion (FF). MWP addition had no influence on prevention of the phase separation observed in the instable group (RF 15). The most notable effect of using MWP was a reduction in apparent viscosity of RF which significantly increased by fat reduction. Moreover, increasing the amount of MWP led to a decrease in the values of consistency index and an increase in the values of flow behavior index. On the other hand, using high amounts of MWP made the emulsion more liquid-like compared to full-fat counterpart. MWP utilization also resulted in similar lightness and yellowness parameters in RF as their full-fat counterparts. MWP in RF increased glossiness and flowability scores, while decreased mouth coating scores in sensory analyses. Fat reduction caused a more compact network, while a porous structure similar to FF was observed with MWP addition to RF. In conclusion, MWP showed a good potential for formulation of reducedfat cheese emulsions with rheological and sensorial characteristics suitable to be used as the feeding liquid in the spray drying process.