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While the structure images of materials have a variety of shapes, the Betti number is independent of their shapes.
Grange, Metallurgical and Materials Trans.
Shibukawa: Investigation of wear in induction–heated AISI E 52100 steel bars under reciprocating motion, International Journal of Materials and Product Technology 44 (3/4), pp. 240-251. (2012) [6] K.
Kida, Homology estimate of grain size easurement based on the JIS samples, Advanced Materials Research, Vol. 813, pp. 120-123. (2013) [13] K.
Mrozek, Computational homology, Applied Mathematical Sciences’, Vol. 157, Heidelberg, Springer-Verlag. (2004)

Fatigue & Fracture of Engineering Materials &Structures.
Applied Surface Science.
Materials Research Express.
Journal of Materials Engineering and Performance.
Materials Chemistry & Physics.

Currently, carbon-based materials have been added to TiO2 photoanodes to improve solar cells performance [2].
Capilla, Materials for Photovoltaics: State of Art and Recent Developments, Int.
Ho, Use of organic materials in dye-sensitized solar cells, Materials Today. 20 (2017) 267-283
Nuroctaviani et al, The Addition of Reduced Graphene Oxide Layer to TiO2 Photoanode of DSSC Using UV Oven Spraying Method, Key Engineering Materials 860 (2020) 15-21
Aksay, Graphene materials and their use in dye-sensitized solar cells, Chem. 114 (2014) 6323-6348

The process of starch consolidation is a modern technique, related to production of new materials, with great possibilities of technological applications, which has drawn attention due to papers published since 1998 [1-8].
Materials and Methods Materials.
The materials were carried to the oven so that the gelling process at 70ºC could take place, during 2 h.
Journal of the European Ceramic Society Vol.18 (1997) p.131-140 [2] R.S.
Mota: Alumina Porous Ceramics: Mathematical Behavior at Different Commercial Starch Concentration Materials Science Forum Vol. 591-53 (2008), p. 442-447 [3] A.F.

Rammed earth construction materials is the most ideal material which could keep material flow and energy flow in natural ecological system balance.
In this paper, the author analyzed the existence value of rammed earth construction from ecological characteristics, building materials, building characteristics as well as other aspects, and expected to provide some references and suggestions for its development and heritage.
The randomness of materials selection The mechanical properties of rammed earth wall mainly affected by the composition, chemical constitution, particle size distribution and physical properties of the earth.
Especially for the underdeveloped central and western regions in China, based on the new style dwellings introduced, there is also a urgent need for develop economically affordable housing, which should be a systematic combination of local materials, appropriate techniques and specialized design.
Journal of Xi'an University of Architecture & Technology, 2001, 33(2):147-149.

Implementation of a constitutive model for the mechanical behavior of TWIP steels and validation simulations Andrea Erhart1, a*, André Haufe1,b, Alexander Butz2, Maksim Zapara2, Dirk Helm2 1DYNAmore GmbH, Industriestr.2, 70565 Stuttgart, Germany 2Fraunhofer Institute for Mechanics of Materials IWM, Freiburg, Germany aae@dynamore.de, bah@dynamore.de Keywords: TWIP-steel, constitutive model, simulation Abstract.
Hence determined anisotropy material parameters αi: bottom.
Chin, State of the knowledge on TWIP steel, Materials Science and Technology, 28 (2013), 513-527
Zapara et al.: Macroscopic modelling and simulations of material behaviour of modern twinning-induced plasticity steels.
Barlat et al.: Plane stress yield stress yield function for aluminum alloy sheets – part1, Theory, International Journal of Plasticity, 19 (2003), 1-23

Cellulose powder from recycled materials can be applied in various fields of industry, including the fabrication of wood-polymer composites [1, 2].
Introduction High quality materials based on cellulose fibers are in high demand in many fields, mainly in paper production and in medicine.
Sources of these fibers are renewable raw materials, such as wood or cotton.
Materials and Methods Obtaining Cellulosic Powder.
Maskavs, Cellulose-Containing Fillers for Polymer Composites, Mechanics of Composite Materials. 39(2) (2003) 183-188

To this date the copper oxide-based materials remain as the highest transition temperature superconductor under normal pressure.
The common family of cuprate-based high temperature superconductor (HTSC) are the Y-based, Bi-Based, Tl-based and Hg-based materials.
Materials and Methods The samples were prepared by using the solid state reaction route.
Tee, Effectiveness of Bi versus Pb on the superconducting properties of the TlSr2CaCu2O7 (1212) phase, Journal of Materials Science Letters 17 (1998) 103-106
Abd-Shukor, Formation of Tl0.85Cr0.15Sr2CaCu2O7 superconductor from ultrafine co-precipitated powders, Materials Letter 60 (2006) 734-736

The lower total PEI/kg (7.45E-01) of the base case illustrates that the material utilization efficiency of the base case is better than that of the heat pump which PEI/kg is 8.14E-01.
Table 1: Cost and exergy analysis Table 2: Product purity Alternatives Base case Heat pump Steam rate kg/hr 573.36 315.56 Reflux ratio 0.586 0.620 TAC [$/y] 279, 000 302, 000 nth % 14.30 18.47 Exergy loss kW 49.92 45.31 PEI/kg 7.45E-01 8.14E-01 Product purity Base case Heat pump Distillate compositions mass % Xwater<10 % 2.19 2.75 Xacetone<50 % 55.9 63.20 Distillate compositions mass % Xmethanol<2 % 1.48 1.67 Xacidity<3 % 2.49 2.69 The lower total PEI/kg (7.45E-01) of the base case illustrates that the material utilization efficiency of the base case is better than the heat pump (PEI/kg 8.14E-01).
References [1] Olujic, Z., Fakhri,F., de Rijke, A., de Graauw, J., Jansens, P.J., Internal heat integration the key to an energy-conserving distillation column, Journal of Chemical Technology and Biotechnology, 2003, 78:241–248,
[4] Ishida M., Taprap R., Graphical Exergy Analysis of processes in Distillation Column by Energy – Utilization Diagrams, AIChE Journal, Vol. 42, No.6.,1996
[5] Rivero R., Koeijer G, Entropy production and exergy loss in experimental distillation columns, Chemical Engineering Science, 2003, 58, 1587 – 1597

Taoyuan, Taiwan 2 Materials & Electro-Optics Research Division Chung-Shan Institute of Science & Technology , Taoyuan, Taiwan a ccf@cc.ncu.edu.tw, b 953403001@cc.ncu.edu.tw, c 983407003@cc.ncu.edu.tw Keywords: LED direct-lit backlight module, diffuser sheet, optical microstructures Abstract.
Both material of upper and lower structures are polycarbonate(PC) which distribute on the surfaces of substrate sheet (PET).
Chou: Fabrication of an antireflective polymer optical film with subwavelength structures using roll-to-roll micro-replication process, Journal of Micromechanics and Microengineering, Vol. 18, (2008) pp. 1-9