the relationship between relaxation and rhythmic exercises with regard to functional neuroplasticity mechanism is a subject that has been studied in recent researches. the purpose of this study was to investigate the effect of rhythmic exercises on the depth of relaxation in national judo athletes. 30 male athletes of national judo team were randomly selected and divided into three groups: cont...

1. a) Compute the Stiefel-Whitney classes of the tangent bundle of RP . (Use the method from class for the tangent Chern classes of complex projectives spaces.) b) Conclude that if the tangent bundle is trivial, then n = 2 − 1 for some m. (In fact n must be 0, 1, 3, 7, but this is much harder to prove; one proof uses the Bott periodicity theorem.) c) Deduce (very easily!) a complete characteriz...

Solution Sketch. This is similar to something done in Lecture 7. Let R be the relation that defines an NP search problem. Define the language L that contains all the pairs (x, z) such that z is the prefix of a solution zz′ such that (x, zz′) ∈ R. Under the assumption that P = NP, there is a polynomial time algorithm A that decides L. Now, given x, we can construct a solution y such that (x, y) ...

Exercise 1. Design a Huffman code for the outcome of a fair die. Evaluate the average length, and compare it against the source entropy. For which source distribution this would be an optimal code? Exercise 2. Let p be the probability of head in a sequence of tosses of a biased coin. A sequence of messages is parsed using the alphabet X = {h, th, tt}. Evaluate H(X) in bits/message and also in b...

4. Describe the D-module extD(M,D) in terms of generators and relations. 5. Prove that extD(M,D) is a 1-dimensional Q(a, k, ω, ζ)-vector space. Give a basis ρ(Λ) of extD(M,D), where ρ : D 3 −→ D3/(RD4) denotes the canonical projection. 6. Deduce that ρ(Λ) generates extD(M,D), i.e., ext 1 D(M,D) is a cyclic D-module. 7. Consider the matrix P = (R − Λ) ∈ D3×5. Show that P admits a left-inverse ov...

General rules for solving exercises This is a theory course, which means: if an exercise does not explicitly say \you do not need to prove your answer" or \justify intuitively", then a formal proof is always required. All exercises and their solutions, no matter whether they are graded or regular/optional ones, are part of the material relevant for the two exams. Some of the exercises are marke...

This ring structure is complicated. In particular it is not the product structure. However, this way of defining the Witt vectors gives us a useful approach for how to prove things about them. Roughly speaking, to prove something about W(A) one can use the ghost map to transfer the problem to the ring A with its product structure. This works especially well if A is p-torsion free since then con...

Study Design: Single-group repeated-measures design. Objectives: To investigate the ability of the wall slide exercise to activate the serratus anterior muscle (SA) at and above 90° of humeral elevation. Background: Strengthening of the SA is a critical component of rehabilitation for patients with shoulder impingement syndromes. Traditional SA exercises have included scapular protraction exerc...

BACKGROUND Gluteus medius (GM) dysfunction is associated with many musculoskeletal disorders. Rehabilitation exercises aimed at strengthening GM appear to improve lower limb kinematics and reduce pain. However, there is a lack of evidence to identify which exercises best activate GM. In particular, as GM consists of three distinct subdivisions, it is unclear if GM activation is consistent acros...

STUDY DESIGN This study used a prospective, single-group repeated-measures design to analyze differences between the electromyographic (EMG) amplitudes produced by exercises for the trapezius and serratus anterior muscles. OBJECTIVE To identify high-intensity exercises that elicit the greatest level of EMG activity in the trapezius and serratus anterior muscles. BACKGROUND The trapezius and...