Digital homotopic distance between digital functions

[EN] In this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as being digitally homotopy invariance.The author would like to thank Tane Vergili and the referees for their helpful suggestions. In particular, the author would like to thank the referee who contributed Proposition 3.2 and Example 4.3.Borat, A. (2021). Digital homotopic distance between digital functions. Applied General Topology. 22(1):183-192. https://doi.org/10.4995/agt.2021.14542OJS183192221C. Berge, Graphs and Hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish Journal of Mathematics 42, no 1 (2018), 1845-1852. https://doi.org/10.3906/mat-1801-94A. Borat and T. Vergili, Higher homotopic distance, Topological Methods in Nonlinear Analysis, to appear.L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15 (1994), 883-839. https://doi.org/10.1016/0167-8655(94)90012-4L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vision, 24 (2006), 167-175. https://doi.org/10.1007/s10851-005-3619-xL. Boxer, Alternate product adjacencies in digital topology, Applied General Topology 19, no. 1 (2018), 21-53. https://doi.org/10.4995/agt.2018.7146O. Cornea, G. Lupton, J. Oprea and D. Tanre, Lusternik-Schnirelmann Category, Mathematical Surveys and Monographs, vol. 103, American Mathematical Society 2003. https://doi.org/10.1090/surv/103M. Farber, Topological complexity of motion planning, Discrete and Computational Geometry 29 (2003), 211-221. https://doi.org/10.1007/s00454-002-0760-9S. E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (2005), 73-91. https://doi.org/10.1016/j.ins.2004.03.018M. Is and I. Karaca, The higher topological complexity in digital images, Applied General Topology 21, no. 2 (2020), 305-325. https://doi.org/10.4995/agt.2020.13553I. Karaca and M. Is, Digital topological complexity numbers, Turkish Journal of Mathematics 42, no. 6 (2018), 3173-3181. https://doi.org/10.3906/mat-1807-101E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conference on Systems, Man, and Cybernetics (1987), 227-234.G. Lupton, J. Oprea and N. A. Scoville, Homotopy theory in digital topology, ArXiv: 1905.07783.G. Lupton, J. Oprea and N. A. Scoville, Subdivisions of maps of digital images, ArXiv: 1906.03170.E. Macias-Virgos and D. Mosquera-Lois, Homotopic distance between maps, Math. Proc. Cambridge Philos. Soc., to appear.G. Sabidussi, Graph multiplication, Math. Z. 72 (1960), 446-457. https://doi.org/10.1007/BF01162967T. Vergili and A. Borat, Digital Lusternik-Schnirelmann category of digital functions, Hacettepe Journal of Mathematics and Statistics 49, no. 4 (2020), 1414-1422. https://doi.org/10.15672/hujms.55979

A NEURAL NETWORK BASED TRAFFIC-FLOW PREDICTION MODEL

Prediction of traffic-flow in Istanbul has been a great concern for planners of the city. Istanbul as being one of the most crowded cities in the Europe has a rural population of more than 10 million. The related transportation agencies ill Istanbul continuously collect data through many ways thanks to improvements in sensor technology and communication systems which allow to more closely monitor the condition of the city transportation system. Since monitoring alone cannot improve the safety or efficiency of the system, those agencies actively inform the drivers continuously through various media including television broadcasts, internet, and electronic display boards on many locations on the roads. Currently, the human expertise is employed to judge traffic-flow on the roads to inform the public. There is no reliance on past data and human experts give opinions only on the present condition without much idea on what will be the likely events in the next hours. Historical events such as school-timings, holidays and other periodic events cannot be utilized for judging the future traffic-flows. This paper makes a preliminary attempt to change scenario by using artificial neural networks (ANNs) to model the past historical data. It aims at the prediction of the traffic volume based on the historical data in each major junction in the city. ANNs have given very encouraging results with the suggested approach explained in the paper

A neural network based traffic-flow prediction model

Prediction of traffic-flow in Istanbul has been a great concern for planners of the city. Istanbul as being one of the most crowded cities in the Europe has a rural population of more than 10 million. The related transportation agencies in Istanbul continuously collect data through many ways thanks to improvements in sensor technology and communication systems which allow to more closely monitor the condition of the city transportation system. Since monitoring alone cannot improve the safety or efficiency of the system, those agencies actively inform the drivers continuously through various media including television broadcasts, internet, and electronic display boards on many locations on the roads. Currently, the human expertise is employed to judge traffic-flow on the roads to inform the public. There is no reliance on past data and human experts give opinions only on the present condition without much idea on what will be the likely events in the next hours. Historical events such as school-timings, holidays and other periodic events cannot be utilized for judging the future traffic-flows. This paper makes a preliminary attempt to change scenario by using artificial neural networks (ANNs) to model the past historical data. It aims at the prediction of the traffic volume based on the historical data in each major junction in the city. ANNs have given very encouraging results with the suggested approach explained in the paper. © Association for Scientific Research

Directed topological complexity of spheres

Open access via Springer compact agreement. Acknowledgements The first author wishes to thank the University of Aberdeen for their hospitality during her stay at the Institute of Mathematics, where this work was carried out. Both authors wish to thank Eric Goubault for useful discussions and for sharing with them preliminary versions of his results, and the anonymous referees for valuable comments.Peer reviewedPreprintPublisher PD

Bir şirket için insan kaynaklarına ilişkin uygulama

Bu makalede Scrum yönteminin bir şirketin İnsan Kaynakları Bölümüne uygulanması incelenmektedir. Ortalama pozisyon kapatma süresi Scrum yöntemini kullanmadan önce 45 gün oldu. Scrum yöntemi şirketin İnsan Kaynakları Bölümünde 2 yıl kullanıldı. Yöntemin kullanılmasıyla sürede 15 günlük bir azalma elde edildi. Scrum yöntemi insanların mümkün olan en yüksek değere sahip ürünleri üretken ve buluşçu bir şekilde geliştirirken karmaşık ve adaptasyona açık sorunları ele alabildikleri bir çerçeve sağlamaktadır. Bu yöntemin temelinde deneysel süreç kontrol teorisi yer almaktadır

Türkiye diyatomitlerinin özellikleri ve filtrasyon karakteristikleri

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1992Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1992Bu Çalışmada muhtelif sıvıların arıtılması işlemlerinde kullanılan diyatomit maddesinin fiziksel, kimyasal ve filtrasyon karakteristiklerinin incelenmesi hedeflenmiştir. Bilindiği gibi yeryüzünde içilip kullanılabilir temiz su miktarı giderek azalmakta, buna karşılık nüfus hızla artmaktadır. Dolayısıyla filtrasyon işlemlerine, özellikle filtre malzemelerine olan ihtiyaç da artmaktadır. içme veya kullanma sularındaki bulanıklık ve rengin düzeltilmesi; demir ve manganezin giderilmesi, bazı mikroorganizmaların tutulması ve bunlara bağlı olarak tad ve kokunun iyileştirilmesi ve radyoaktif bulaşmanın giderilmesinde diyatomit filtrasyon metodu önemli bir yer tutmaktadır. Filtrasyonda kullanılan diyatomit ham olarak doğada bulunmaktadır. Ham diyatomit fiziksel ve/veya kimyasal olarak işlem gördükten sonra kullanılabilir hale getirilmektedir. Birinci bölümde diyatomitin ve diyatomit filtrasyonun öneminden bahsedilmektedir. ikinci bölümde diyatomit hakkında genel bilgiler verilmiş, kullanılış yerleri, diyatomitin oluşma şartları açıklanmış, daha sonra Türkiye'de ve dünyadaki diyatomit üretimi ve fiyatları belirtilmiştir. üçüncü bölümde Türkiye'deki diyatomitlerin oluşumlarına ilişkin bilgiler sunulmuş, gezilip incelenen 13 rezerv tanıtılmıştır. Dördüncü bölümde Türkiye'deki diyatomitlerin fiziksel ve kimyasal özelliklerinin belirlenmesinde kullanılan metodlar açıklanmış, daha sonra uygulanan deney ve analizler neticesinde belirlenen fiziksel ve kimyasal nitelikler verilmiştir. Beşinci bölümde gözenekli ortam hidrodinamiği ve Darcy kanunu incelenmiş, diyatomit filtrasyonda filtre direnci ve sabit basınçta süzüntü hacminin değişimi, filtre keki içindeki ortalama gözeneklilik bağıntıları belirlenmiş, belirli bir andaki porozite dağılımının hesabı gösterilmiş ve sayısal örnek verilmiştir. The requirment for treatment of drinking and potable waters of small villages, rural residential areas, field- based military units, industrial water demand and the need for treating the waters of swimming pools is becoming increasingly important in Turkey in the last decade. Diatomite filtration has a significant place in water treatment processes in the removal of iron and raanganese, improving turbidity and color, removal of certain microorganisms resulting in the improvement of taste and odor, and preventing radioactive contamination. Therefore, there will be an increasing need for the diatomite material. The diatomite used in filtration is found as raw in nature. Raw diatomite is made usable after being cleaned physically and/or chemically. in this work, numereous and sufficiently large diatomite reserves has been identified in Turkey. At the present, diatomite earth and diatomite fi iter material is being imported into Turkey under different names. in the first part of this work, general information about diatomites, its formation, factors affecting its development, diatomite production and prices in Turkey and in the world has been învestigated. Payments for the raw, processed and product diatomite which was imported into Turkey in 1990 amount to 3.5 million U.S. dollars. Considering the rate of increase and the development of Turkey, this quantity will exceed 5 million U.S. dollars in the raiddle of the 1990's. Diatomite deposits of the world having commercial value were formed between the Third and the glacial period of the Fourth era. Although most of the diatomites in Turkey are in Neocene in age, the age of some diatomites are determined as Miocene. xi Known diatomite deposits of Turkey were forraed in fresh water lakes which were cut by volcanic material. So that diatomites gained necessary SiOa för their shells from the silicates in volcanic material. The number and the reserve of diatomite deposits existing in Turkey might be larger than known since Anatolia had wide Miocene land and extensive extrusive volcanism in that area. Within the framework of this study, diatomite deposits in Turkey have been investigated at site, and samples have been taken frora 13 sites in "Afyon-îscehisar- Seydiler, Ankara-Ayaş-Başbereket, Ankara-Ayaş-Gücügöz Deresi, Ankara-Kızılcahamam-Beşkonak, Çanakkale-Çan- Keçiagılı, Çankırı-Çerkeş-Akhasan, Cankırı-Orta-Karaagaç, Cankırı-Orta-Bastak, Denizi i-Sarayköy-Karakıran, Denizii-Sarayköy-Aşağı Tırkaz, Kayseri-Merkez-Hırka, Kütahya-Merkez-Alayunt and Uşak-Merkez-Kayaagıl". Diatomite should have certain characteristics according to its usage. The methods and experimental techniques used for the microscopic examination and the determination of physical and chemical characteristics have been explained. Following physical and chemical properties of diatomite samples have been determined, the specific weight of diatomite, bulk density (apparent specific weight), porosity, adsorption capability, volume weight, partide size distribution, filtration resistance factor, determination of silicon, aluminiura, iron, calcium and magnesium content. Specific weights are 1,931-2,381 gr/cnr3, bulk densities (apparent specific gravities) 0,453-0,882 gr/cm°" porosities 0,57-0,83, adsorbtion capabilities in weight 129-197 %, volume weights 0,37-0,47 gr/cm=*. Particle-size distribution of the uncalcined raw diatomites are between 5-100 microns in diaraeter. Filtration resistance factors are a = 2,75xlO'5' -1560xlO'3' s/m*. Chemical analyses are as follows: SiOz 65,42-87,48 %, AlaOoı 0,81-3,42 %, Fe=.O3 0,64-2,48 %, MgO 0,39-7,20 % and CaO 0,71-9,37 %. Ignition losses in weight at 900°C are 3,54-13,42 %. And pH are 6,75-9,5. 20 samples frora each deposit were prepared as permanent preparation on glass si ide for microscopic examination. Navicula, Cvm.bel la, Melosira, Svnedra and other diatom genera have been found in Turkish diaomites. The above mentioned characteristics are similar to xii characteristics of the diatomites which produced in other countries and imported to Turkey. Physical and chemical characteristics and microscopic structures indicate that Turkish diatomites are feasible, in a large area, as materials for filter-aid, construction, insulation, absorbing, filling and polishing. in constant pressure filtration, constant cake resistance can be accepted as the most simple approximation. However, it is observed that this approKimation is valid for short filtration period. For long filtration period, the change in porosity should be taken into account. in this work, it has been observed that even for a pressure of as low as 2 bars, porosity decreased by 10 % in 6 minutes. Porosity varies along the cake as a function of time and cake thickness. The porosity and specific resistance of the infinetesimally thick layer at the outermost surface of the cake corresponds to zero compression pressure. With every fresh cake layer that comes, porosity at a given point decreases, thickness of the cake increases. As the pressure drop along the cake increases, average porosity decreases. Depending on the maximum pressure applied it is obvious that a minimum porosity will be reached. Asuming that the porosity within the cake changes with thickness x and time t, the "local and instantaneous porosity" n«..M=n(x,t) at any point x and at time t; when the relations between the average cake porosity, n-fe.=n(x*,t) at a given time and the porosity attained at the end of the overall filtration, n=n(n«.,t) are investigated, it has been shown that with the help of the experimental data, calculation of local and instantaneous porosity n*.« is possible. Three approximations have been taken into consideration for the determination of local and instantaneous porosity. in the first approxiraation, the cake water has been neglected and the concentration of the slurry över the cake assumed constant. in this case, n*.. " values can be calculated f rom time, cake thickness and filtrate volume which is determined experimentally. in the second approximation, an expression has been developed which is based on the dried weight of the cake and cake thickness and n«..« has been found. in the third approximation, the slurry concentration has been taken constant as in the first case; but n*., « has been calculated without neglecting the cake water. Two methods have been used for the determination of local and instantaneous porosity by applying the results xiii of the experimental runs to the three approximations. The first method is numerical solution. The equations which were developed for the purpose have been expressed as finite differences and experimental results applied. The second method is analytical solution. In order to develop the necessary relations for the analytical solution, first the experimental data have been converted to three types of functions. Two of these are power functions, one is logarithmic type. The least square method has been applied for curve fitting and it has been found that the curve represented by the function x=a«tto" is the best representation according to the regression analysis. Similarly, variations of average porosity have been determined. With the help of these data which were continuously obtained, analytical solutions have been attained. In this work, local and instantaneous porosity values could be expressed in terms of time and cake thickness, and three dimensional figures have been obtained. These figures demonstrate various characteristics of the cake. For example, it is observed that there is nearly an exponential reduction in the porosity due to compaction of the cake layer at the surface determined by time (t) and the porosity (n) axes and where (x) equals zero, that is, at the cake layer adjacent to the filter septum. Various investigations are made for porous media in micro and macro scale. Subjects such as viscous flow, particle shapes, compaction of cakes, multi-phase flow, diffusion and reactive flow are been investigated in the fields of environment, soil mechanics, coal, petroleum and mining. In these investigations, either porosity values are used, or approximations are made by models based on porosity values. By the method which is presented in this work, it will be possible to use the local and instantaneous porosity results necessary for the investigations mentioned above. Also the results of this work will be helpful in mathematical modelling and simulation investigations for particle array and flow around a particle both for correction and for the purpose of comparison. In order to apply the model proposed in this study for the variation of local and instantaneous porosity in porous media, it is necessary to develop an experimental set up which will make it easier to take the sample outside. These experiments were made at a constant pressure of 2 bars. Pollution sources, that is bacteria and other material have not been added to the slurry. It will be useful to investigate the behaviour of the diatomite under different pressures and by adding different pollution sources. xiv It is possible to apply mathematical modelling and simulation investigations on the array of sand particles and the flow around them to diatomites having different microstructure. With the methods developed in this work, it is possible to compare the results of theoretical modelling, and even by correcting the results obtained by theoretical modelling, to obtain the correct values. Thus, by using models based on computerized calculations instead of experimental methods, it will be possible to save time and money.DoktoraPh.D