Abstract: An eyeglass-type video display device includes a video generation device and an eyeglass body. The video generation device includes a MEMS optical deflector and a VCSEL mounted on the same substrate, and a planar mirror and a rotating mirror arranged above the substrate. Light emitted from an emission part is emitted obliquely upward from one longitudinal-direction end side of the substrate through the planar mirror, the rotating mirror, and a revolving mirror. The video generation device is attached to an arm of the eyeglass body such that the emission direction of the light becomes a direction that is obliquely forward with respect to an inner side surface of the arm.

Abstract: An optical scanning device includes a standing plate part which has an inclined groove and a through hole at positions above a vertical cavity surface emitting laser (VCSEL) and a micro electro mechanical systems (MEMS) optical deflector, and which is fixed to a substrate. A plate-shaped mirror and a rotary mirror have one end portions thereof in the Y-axis direction supported by the inclined groove and the through hole, respectively. The through hole has the shape of a rotating body having an axis in the Y-axis direction as the centerline thereof.

Abstract: A method for realization of samples of random numbers distributed on temporal and spatial lattice points is described. The method may include using samples obtained by integrating a temporal and spatial white noise over the temporally smallest unit and over the spatial unit of volume, with the distribution of samples. The method may ensure small correlations to neighboring samples in temporal as well as spatial directions.

Abstract: For any multiplicative congruential generator (d, z) with an odd modulus d and a multiplier z coprime to d, a computationally innovative method is presented as specialized forms of 2nd degree spectral tests of (d, z^i) with 2?i?6, at the least. Providing with sharp and powerful sieving tools, the method enables the excavation of the integer set (d, z) as a generator of uniform and independent random numbers of excellent statistics with sufficiently long periods for simulations, and furnishes the selected generator with ways of clear, unambiguous and quantitative specifications of its performance.

Abstract: For any multiplicative congruential generator (d, z) with an odd modulus d and a multiplier z coprime to d, a computationally innovative method is presented as specialized forms of 2nd degree spectral tests of (d, z?i) with 2?i?6, at the least. Providing with sharp and powerful sieving tools, the method enables the excavation of the integer set (d, z) as a generator of uniform and independent random numbers of excellent statistics with sufficiently long periods for simulations, and furnishes the selected generator with ways of clear, unambiguous and quantitative specifications of its performance.

Abstract: The present invention discloses a new method of spectral tests, on multiplicative congruential generator (d,z,n) or (d,z) comprising an odd integer d for the modulus and an integer z coprime with d for the multiplier and an integer n coprime with d for the seed and generating the sequence of integers {nk:?nzk?1 mod(d)|1?nk?d, k=1,2, . . . } consecutively and giving the output random number sequence by realizing the arithmetic {vk:=nk/d|0?vk?1, k=1,2, . . . }, the new method being based on the valuation of the geometrical form of the lattice GL(d,z), wherein L consecutive integer outputs of the generator (d,z,n) {Qk:=(nk,nk+1, . . . ,nk+L?1)|k=1,2, . . .

Abstract: An invention is presented with new and simple ways of spectral tests applicable to the multiplicative congruential generator (d,z) with any odd modulus d and any multiplier z coprime to d. The invention realizes powerful ways to select multipliers of excellence with greatly improved statistical performances in their generation of uniform and independent random numbers. Related two inventions for new designs of the generator (d,z) are presented at the same time, as strongly facilitative for the application of advocated extended spectral tests, by exploiting specific structures of moduluses formed by two odd-prime-powers so as to realize improved periodic structures that are set conveniently out of tune avoiding harmful resonances.

Abstract: A system and method of generating uniform and independent random numbers is given by comprising two distinct odd primes that give an odd integer and an even integer, together with by taking an integer exponent and an integer exponent, by forming the composite modulus by taking a primitive root modulo and a primitive modulo and giving the multiplier modulo by either the system of congruence relations, any of which determines the multiplier modulo uniquely, by taking an initial value coprime. The method generates the sequence of integers by recursive congruence relations and gives an output of uniform and independent random numbers.

Abstract: A method of obtaining uniform and independent random numbers is given (a) comprising two distinct odd primes p1, p2 that give mutually coprime integers q1=(p1?1)/2 and q2=(p2?1)/2 with different parity to form the modulus d=p1p2; (b) comprising primitive roots z1, z2 of primes p1, p2, respectively, giving congruence relations z?zj mod(pj) for j=1, 2 that determine the multiplier z; and (c) comprising the initial value n coprime with d=p1p2. The method generates the coset sequence n<z>={r1=n, r2, r3, . . . } of period T=2q1q2 recursively by rj+1=zrj mod(d) for j=1, 2, . . . in the reduced residue class group Z*d, giving {v1=r1/d, v2=r2/d, . . . } for output.

Abstract: A method of obtaining uniform and independent random numbers is given 1. by taking two distinct odd primes p1,p2 that give mutually coprime integers, an odd q1=(p1?1)/2 and an even q2=(p2?1)/2, to form the modulus d=p1p2, 2. by taking primitive roots z1,z2 of primes p1,p2, respectively, and giving congruence relations z??z1 mod (p1) and z?z2 mod (p2) that determine the multiplier z uniquely modulo d, and 3. by taking an initial value n coprime with d=p1p2. The method generates the sequence of integers {rj|1?j?T=2q1q2} recursively by congruence relations r1?n mod(d), rj+1?zrj mod (d), 0<rj<d, 1?j?T=2q1q2, and gives {v1=r1/d,v2=r2/d, . . . } for output of uniform and independent random numbers.

Abstract: A method of obtaining uniform and independent random numbers is given (a) comprising two distinct odd primes p1, p2 that give mutually coprime integers q1=(p1?1)/2 and q2=(p2?1)/2 with different parity to form the modulus d=p1p2; (b) comprising primitive roots z1, z2 of primes p1, p2, respectively, giving congruence relations z?zj mod (pj) for j=1, 2 that determine the multiplier z; and (c) comprising the initial value n coprime with d=p1p2. The method generates the coset sequence n<z>={r1=n, r2, r3, . . . } of period T=2q1q2 recursively by rj+1=zrj mod (d) for j=1, 2, . . . in the reduced residue class group Z*d, giving {v1=r1/d, v2=r2/d, . . . } for output.