where U = {1, 2, . . . , n}. Example. Suppose we ask how many integers less than 120 are relatively prime to it. Since 120 has prime factors 2, 3, and 5, any number that is relatively prime to it is not a multiple of any of these. We can solve this using the Inclusion-Exclusion Principle as follows. Let A = {1, 2, . . . , 120}, the set of integers from 1 to 120. Let S1 be the multiples of 2 in ...

A 53-year-old patient with chronic hepatitis C virus infection was referred because of the presence of multiples ultrasonographic images simulating liver metastasis. Physical examination was normal. Liver function test showed increased levels of aminotransferases, high levels of γ-glutamyltransferase and normal alkaline phosphatase. Liver ultrasound identified multiples nodules that measured 0....

The article examines the market valuation approach using industry multiples as this method has recently attracted increasing interest from appraisers. It investigates whether constructing one’s own for company which are based on a provides better results than Damodaran’s in terms of resulting accuracy. study uses sample 162 German companies publicly traded 2010–2019 and analyses some most frequ...

The advances in reproductive technologies have changed the demographics of multifetal pregnancies. In the first trimester, ultrasound allows to diagnose the number of multiples, chorionicity and amnionicity, the presence or absence of nuchal translucency, early growth discordance, severe malformations and the origin of activities and contacts between multiples. In the second and third trimester...

The action to grasp an object by a human hand comprises not only an eye-hand coordination, but also a motion process that controls and plans the movement for grasping objects. To understand this behavior, it is necessary to study eye and hand movements simultaneously. A novel approach to understand the user’s intentions with computer vision technics is proposed in this paper. Our solution perfo...

Algebraic attacks have received a lot of attention in studying security of symmetric ciphers. The function used in a symmetric cipher should have high algebraic immunity (AI) to resist algebraic attacks. In this paper we are interested in finding AI of Boolean power functions. We give an upper bound on the AI of any Boolean power function and a formula to find its corresponding low degree multi...

Multiple attenuation in complex geology remains a very intensive research area. The proposed technique aims to use the spatial predictability of both the signal (primaries) and noise (multiples) in order to perform the multiple attenuation in the time domain. The spatial predictability is estimated with multidimensional prediction-error filters. These filters are time-variant in order to handle...

Imaging with seismic data is typically done under the assumption of single scattering. Here we formulate a theory that includes multiply scattered waves in the imaging process. We develop both a forward and an inverse scattering series derived from the Lippmann–Schwinger equation and the Bremmer coupling series. We estimate leading-order internal multiples explicitly using the third term of the...

Two methods for suppressing multiples are proposed. In the first, multiple suppression is expressed as a signal to noise separation problem. The problem is solved in the time domain using space-varying Prediction Error Filters (PEFs). The second method shows how greater separation between primaries and multiples can be obtained by velocity space inversion using a Huber functional rather than th...

A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are multiples of projection bodies. In the equivariant case, the only such valuations are generalized difference bodies combined with multiples of the newly defined disc...