We introduce three deenitions of the q-analogs of Motzkin numbers and illustrate some combinatorial interpretations of these q-numbers. We relate the rst class of q-numbers to the steep parallelogram polyominoes' generating function according to their width, perimeter and area. We show that this generating function is the quotient of two q-Bessel functions. The second class of q-Motzkin numbers...

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First class functions in constrained second class systems. Abstract Generators of the algebra of first class functions in a system with second class constraints are found. It is shown that first class functions form algebras with respect to the Dirac bracket and pointwise multiplication .The subspace of functions vanishing on constraint surface are ideals of these algebras. The corresponding qu...

 There are many methods for the synthesis of logical functions. All these methods can be divided into two classes the first one is Two-Level Logic Synthesis and the second one is Multi-Level Logic Synthesis. The multi-level circuits and their structure are easier for practical realization if there is a large number of variables. In this paper we concentrate on a part of the second class synthe...

In this paper, we study the noise-reduction problem in the KarhunenLoève expansion domain. We develop two classes of optimal filters. The first class estimates a frame of speech by filtering the corresponding frame of the noisy speech. We will show that several well-known existing methods belong or are closely related to this category. The second class, which has not been studied before, obtain...

BACKGROUND Students evaluations of their learning experiences can provide a useful source of information about clerkship effectiveness in undergraduate medical education. However, low response rates in clerkship evaluation surveys remain an important limitation. This study examined the impact of increasing response rates using a compulsory approach on validity evidence. METHODS Data included ...

UNLABELLED The two-arm Clinical Decisions/Diagnostic Workshop (CD/DW) approach to undergraduate medical education has been successfully used in Brazil. OBJECTIVE Present the CD/DW approach to the teaching of stroke, with the results of its pre-experimental application and of a comparative study with the traditional lecture-case discussion approach. METHOD Application of two questionnaires (...

BACKGROUND Teaching basic science courses is challenging in undergraduate medical education because of the ubiquitous use of didactic lectures and reward for recall of factual information during examinations. The purpose of this study is to introduce concept maps with clinical cases (the innovative program) to improve learning of biochemistry course content. METHODS Participants were first ye...

OBJECTIVE To conduct a systematic review of primary research in undergraduate medical education in Pakistan in order to evaluate PBL programs, examine outcomes and competencies influenced by PBL, and compare them with conventional learning (lecture based learning, LBL). STUDY DESIGN Qualitative content analysis. PLACE AND DURATION OF STUDY Rawalpindi Medical College, Rawalpindi, from June 2...

This paper presents a taxonomy of 19 cognitive criteria for judging what constitutes effective representational systems, particularly for knowledge rich topics. Two classes of cognitive criteria are discussed. The first concerns access to concepts by reading and making inferences from external representations. The second class addresses the generation and manipulation of external representation...