Abstract: A determining method of movement sequence and a positioning apparatus of the invention are arranged in such a manner that, in order to measure positions of plural marks as being measurement targets provided on a wafer within a shorter time, a group including executable movement sequences is generated out of a group of movement sequence candidates, each indicating a measurement order of these marks, and a movement sequence that accomplishes a movement operation between the marks within the shortest time is obtained from the group thus generated. For efficiently searching an optical system as a globally optimal solution within a shorter computation time, independently of an initial solution given, a designing method of optical system of the invention obtains the optimal solution of the optical system to be designed, using an evolutionary computation method (genetic algorithm) having a genetic operator for handling continuous values explicitly.

Abstract: A determining method of movement sequence and a positioning apparatus of the invention are arranged in such a manner that, in order to measure positions of plural marks as being measurement targets provided on a wafer within a shorter time, a group including executable movement sequences is generated out of a group of movement sequence candidates, each indicating a measurement order of these marks, and a movement sequence that accomplishes a movement operation between the marks within the shortest time is obtained from the group thus generated. For efficiently searching an optical system as a globally optimal solution within a shorter computation time, independently of an initial solution given, a designing method of optical system of the invention obtains the optimal solution of the optical system to be designed, using an evolutionary computation method (genetic algorithm) having a genetic operator for handling continues values explicitly.

Abstract: A determining method of movement sequence and a positioning apparatus of the invention are arranged in such a manner that, in order to measure positions of plural marks as being measurement targets provided on a wafer within a shorter time, a group including executable movement sequences is generated out of a group of movement sequence candidates, each indicating a measurement order of these marks, and a movement sequence that accomplishes a movement operation between the marks within the shortest time is obtained from the group thus generated.

Abstract: A determining method of movement sequence and a positioning apparatus of the invention are arranged in such a manner that, in order to measure positions of plural marks as being measurement targets provided on a wafer within a shorter time, a group including executable movement sequences is generated out of a group of movement sequence candidates, each indicating a measurement order of these marks, and a movement sequence that accomplishes a movement operation between the marks within the shortest time is obtained from the group thus generated.

Abstract: A hollow fiber fabric comprising hollow fibers having a high hollowness ratio of at least 20% and composed of a polymer of a single composition, and the hollow fibers having slits as traces of a removed polymer and the slits being formed in the longitudinal direction of the fibers in such a state that the slits communicate to hollow portions. The fabric is produced by treating a fabric comprising hollow fibers having a high hollowness ratio of at least 20% and composed of a polymer of a single composition with a solvent or solution which dissolves the polymer, to partially dissolve the polymer at low orientation and/or deformation strain concentrated portions, to form slits as traces of a removed polymer in such a state that the slits communicate to hollow portions, along the longitudinal direction of the hollow fibers.

Abstract: A high heat-resistant synthetic fiber material containing, for example, aramid, PEEK, or PEN fibers, that can be dyed uniformly at a high color density, with a dye dissolved or dispersed in a liquid medium, for example, water, and having a molecular weight of 330 to 400, at a dyeing temperature of 150.degree. C. or more within a closed system.

Abstract: A synthetic fibers having a melting or softening temperature of 160.degree. C. or more, for example, polyester fibers, are dyed with an organic coloring material having a molecular weight of 370 or more, for example, disperse dye, vat dye and phthalocyanine pigment, at a temperature of 150.degree. C. or more, at a high color depth, and the resultant dyed product exhibits a high color fastness to washing or light.

Abstract: A deeply dyed polyester fabric exhibiting a lightness index L* value of 25 to 60. Fibers at least in the surface layer portion of either or both of the warps and wefts exhibit a light transmittance to an extent such that the difference .DELTA.X (%) between the light transmittance X.perp. (%) of polarized light vibrating perpendicular to the fiber axis at a wavelength of the maximum absorption and the light transmittance X .sup.[ (%) of polarized light vibrating parallel to the fiber axis at the same wavelength is not larger than 10%.

Abstract: A polyester fiber having a superior stainproof property comprises at least one fiber-forming polyester copolymer comprising a backbone polyester polymer and at least one type of terminal substituent which blocks at least some of the terminals of the molecules of the backbone polyester polymer and which substituent consists of a polyoxyalkyleneglycol monoether group of the formula (I):R.sup.1 -O--R.sup.2 -O.sub.n (I)wherein R.sup.1 is a monovalent organic radical free from active hydrogen atom, R.sup.2 is an alkylene radical, and n is an integer of 2 or more.

Abstract: An antistatic polyester fabric having a water repellency, which comprises a woven or knitted fabric comprising a fiber of a modified polyester composed mainly of a polyester and blended with an antistatic agent, at least the surface of which is covered with a fluorine type water and oil-repellency agent.

Abstract: A cut pile fabric such as a velvet composed of a synthetic fiber pile having deep color shade and smooth touch on its pile surface, the piles thereof having non-mushroom shaped cut ends at their tip portions, defined by the equation d.sub.1 /d.sub.2 .ltoreq.1.3, where d.sub.1 is the maximum diameter of the tip portion and d.sub.2 is a diameter of the remaining portion of the piles. The pile fabric is obtained by utilizing, as a pile yarn, a synthetic yarn having a breakage strength of less than 2.8 g/De, a primary yielding strength of more than 1.2 g/De, a breakage elongation of less than 50%, and a primary yielding elongation of less than 10%. Such synthetic yarn can advantageously be prepared by a crystallization drawing process.

Abstract: A process for the preparation of a woven fabric of low air permeability which comprises preparing a woven fabric by use of a composite fiber of a splitting and severing type, which consists of polyester and polyamide and produces extremely fine fibers of 0.001 to 0.8 denier size, as a warp and/or a weft; treating thus obtained woven fabric by use of an aqueous emulsion of a swelling agent for polyester and nylon under the conditions where nylon is mainly allowed to swell and then shrink; scouring and dyeing the woven fabric; and after calendering the woven fabric with the use of heated rollers rotated under pressure.