Non-autonomous Svinolupov Jordan KdV Systems

Non-autonomous Svinolupov-Jordan systems are considered. The integrability criteria of such systems are associated with the existence of recursion operators. A new non-autonomous KdV system is obtained and its recursion operator is given for all $N$. The examples for N=2 and N=3 are studied in detail. Some possible transformations are also discussed which map some systems to autonomous cases.Comment: Latex file (amssymb), 10 page

A new integrable generalization of the Korteweg - de Vries equation

A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.Comment: 13 pages, 2 figure

Çapraz Akışlı Hava-Gaz Isı Değiştiricisinin Sonlu Farklar Metodu Kullanılarak Modellenmesi

In this study, temperature distribution and total heat transfer were calculated for two-dimensional cross flow heat exchanger using finite difference method. A cross- flow heat exchanger consists of parallel sheets. While the hot fluid flows from one plate, the cold fluid flows through the next plate with cross geometry. This structure is repeated in many plates. After the differential equation is converted to the finite difference equation, it proceeds in a row by starting from the corner where the two inlet temperatures are known, and thus the temperature profile of the entire heat exchanger is easily reached. Throughout the study, air was used as cold fluid in all analysis. Air and exhaust gases were taken as hot fluid, thus the performance of the heat exchanger was examined. A mathematical model was developed by using the finite difference equations in Java programming language. For example, the temperature profile of a hot air with an inlet temperature of 75 C and the temperature profile of a cold air with an inlet temperature of 20 C were calculated with the aid of the mathematical model and the total heat transfer was determined approximately 45,5 KW.Bu çalışmada çapraz (dik) akışlı ısı değiştiricileri üzerindeki sıcaklık dağılımı ve ısı transferi hesapları iki boyutlu sonlu farklar modeli kullanılarak yapılmıştır. Çapraz akışlı ısı değiştiricileri birbirine paralel levhalardan oluşur ve bir levhadan sıcak akışkan akarken bir sonraki levhadan soğuk akışkan çapraz geometride akar. Bu yapı birçok levha halinde tekrarlanır. Diferansiyel denklem sonlu farklar denklemi haline getirildikten sonra iki giriş sıcaklığının bilindiği köşeden başlamak suretiyle satırlar halinde çözülerek ilerlenir ve bu şekilde tüm ısı değiştiricinin sıcaklık profiline kolaylıkla ulaşılır. Bu çalışma boyunca soğuk akışkan olarak tüm analizlerde hava alınmıştır. Sıcak akışkan olarak ise hava ve yanma gazları alınarak ısı değiştiricinin performansı incelenmiştir. Bu çalışma için sonlu fark denklemleri kullanılarak Java programlama dilinde bir matematiksel model geliştirilmiştir. Örnek olarak 750C giriş sıcaklığına sahip sıcak akışkan ile 200C giriş sıcaklığına sahip soğuk akışkanın sıcaklık profili geliştirilen matematiksel model yardımı ile adım adım hesaplanmış ve toplam ısı transfer değeri de yaklaşık 45,5 KW olarak belirlenmiştir

Modeling of Cross Flow Air-Gas Heat Exchanger Using Finite Difference Method

Bu çalışmada çapraz (dik) akışlı ısı değiştiricileri üzerindeki sıcaklık dağılımı ve ısı transferi hesapları iki boyutlu sonlu farklar modeli kullanılarak yapılmıştır. Çapraz akışlı ısı değiştiricileri birbirine paralel levhalardan oluşur ve bir levhadan sıcak akışkan akarken bir sonraki levhadan soğuk akışkan çapraz geometride akar. Bu yapı birçok levha halinde tekrarlanır. Diferansiyel denklem sonlu farklar denklemi haline getirildikten sonra iki giriş sıcaklığının bilindiği köşeden başlamak suretiyle satırlar halinde çözülerek ilerlenir ve bu şekilde tüm ısı değiştiricinin sıcaklık profiline kolaylıkla ulaşılır. Bu çalışma boyunca soğuk akışkan olarak tüm analizlerde hava alınmıştır. Sıcak akışkan olarak ise hava ve yanma gazları alınarak ısı değiştiricinin performansı incelenmiştir. Bu çalışma için sonlu fark denklemleri kullanılarak Java programlama dilinde bir matematiksel model geliştirilmiştir. Örnek olarak 750C giriş sıcaklığına sahip sıcak akışkan ile 200C giriş sıcaklığına sahip soğuk akışkanın sıcaklık profili geliştirilen matematiksel model yardımı ile adım adım hesaplanmış ve toplam ısı transfer değeri de yaklaşık 45,5 KW olarak belirlenmiştir.In this study, temperature distribution and total heat transfer were calculated for two-dimensional cross flow heat exchanger using finite difference method. A cross- flow heat exchanger consists of parallel sheets. While the hot fluid flows from one plate, the cold fluid flows through the next plate with cross geometry. This structure is repeated in many plates. After the differential equation is converted to the finite difference equation, it proceeds in a row by starting from the corner where the two inlet temperatures are known, and thus the temperature profile of the entire heat exchanger is easily reached. Throughout the study, air was used as cold fluid in all analysis. Air and exhaust gases were taken as hot fluid, thus the performance of the heat exchanger was examined. A mathematical model was developed by using the finite difference equations in Java programming language. For example, the temperature profile of a hot air with an inlet temperature of 75 C and the temperature profile of a cold air with an inlet temperature of 20 C were calculated with the aid of the mathematical model and the total heat transfer was determined approximately 45,5 KW

Assessing the Kinesiophobia and Depression Status at Return to Sport Following Sport Related Injuries in Contact and Non-Contact Sports

Objective: The aim of this study is to examine the levels of kinesophobia and depression following sports injuries in physically contact and non-contact sports. Material and Methods: A total of 130 male athletes from 14 different sports, who were injured at least six months before were included in the study. Individuals participating in the study were interviewed by means of the Beck Depression Inventory and the Tampa Kinesiophobia Scale. Participants were also asked to complete a form to determine the injuries they had experienced. Results: There were no statistically significant differences between the physically contact and non-contact sport groups’ kinesiophobia and depression scores (p>0.05). There was no significant correlation between these two scores (r=0.27, p>0.05). Beck Depression Inventory scores following injuries that occurred in training and competition were significantly higher in physically contact sports than non-contact sports (