Formeln und Lehrsätze zum Gebrauche der elliptischen Functionen : nach Vorlesungen und Aufzeichnungen des K. Weierstrass /

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Formeln und Lehrsätze zum Gebrauche der elliptischen Functionen, nach Vorlesungen und Aufzeichnungen des K. Weierstrass /

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Cerebellar language and cognitive functions in childhood: A comparative review of the clinical research

Background: Recent research addressing evidence from functional neuroimaging studies, neurophysiological research, and new advances in neuropsychology together with traditional cerebellar lesion studies have recently implicated the cerebellum in adult language and cognitive functions. However, more limited information is currently available in describing the functional connectivity present in the paediatric population. Aims: It is the purpose of this paper to review recent clinical research pertaining to paediatric populations, outlining the impact of site of lesion and specific associated clinical changes in children with cerebellar disturbances. Main contribution: The specific contribution of the right cerebellar hemisphere to language function is identified to also exist in the paediatric population, highlighting the existence of functional connections between this region of the brain and left frontal cortical areas early in development. Conclusions: Implications for future research in paediatric populations are extensive, as a greater awareness and an understanding of the recently acknowledged involvement of the cerebellum in cognition and nonmotor linguistic function is anticipated to also add new dimension and direction to the analysis of childhood language outcomes associated with the cerebellum.

C-terminal charged cluster of MscL, RKKEE, functions as a pH sensor

The RKKEE cluster of charged residues located within the cytoplasmic helix of the bacterial mechanosensitive channel, MscL, is essential for the channel function. The structure of MscL determined by x-ray crystallography and electron paramagnetic resonance spectroscopy has revealed discrepancies toward the C-terminus suggesting that the structure of the C-terminal helical bundle differs depending on the pH of the cytoplasm. In this study we examined the effect of pH as well as charge reversal and residue substitution within the RKKEE cluster on the mechanosensitivity of Escherichia coli MscL reconstituted into liposomes using the patch-clamp technique. Protonation of either positively or negatively charged residues within the cluster, achieved by changing the experimental pH or residue substitution within the RKKEE cluster, significantly increased the free energy of activation for the MscL channel due to an increase in activation pressure. Our data suggest that the orientation of the C-terminal helices relative to the aqueous medium is pH dependent, indicating that the RKKEE cluster functions as a proton sensor by adjusting the channel sensitivity to membrane tension in a pH-dependent fashion. A possible implication of our results for the physiology of bacterial cells is briefly discussed.

Spatial contrast sensitivity and external noise: applications to optical and neural modulation transfer functions

The thesis will show how to equalise the effect of quantal noise across spatial frequencies by keeping the retinal flux (If-2) constant. In addition, quantal noise is used to study the effect of grating area and spatial frequency on contrast sensitivity resulting in the extension of the new contrast detection model describing the human contrast detection system as a simple image processor. According to the model the human contrast detection system comprises low-pass filtering due to ocular optics, addition of light dependent noise at the event of quantal absorption, high-pass filtering due to the neural visual pathways, addition of internal neural noise, after which detection takes place by a local matched filter, whose sampling efficiency decreases as grating area is increased. Furthermore, this work will demonstrate how to extract both the optical and neural modulation transfer functions of the human eye. The neural transfer function is found to be proportional to spatial frequency up to the local cut-off frequency at eccentricities of 0 - 37 deg across the visual field. The optical transfer function of the human eye is proposed to be more affected by the Stiles-Crawford -effect than generally assumed in the literature. Similarly, this work questions the prevailing ideas about the factors limiting peripheral vision by showing that peripheral optical acts as a low-pass filter in normal viewing conditions, and therefore the effect of peripheral optics is worse than generally assumed.

On some Generalizations of a Class of Discrete Functions

In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.

On Averaging Null Sequences of Real-Valued Functions

If ξ is a countable ordinal and (fk) a sequence of real-valued functions we define the repeated averages of order ξ of (fk). By using a partition theorem of Nash-Williams for families of finite subsets of positive integers it is proved that if ξ is a countable ordinal then every sequence (fk) of real-valued functions has a subsequence (f'k) such that either every sequence of repeated averages of order ξ of (f'k) converges uniformly to zero or no sequence of repeated averages of order ξ of (f'k) converges uniformly to zero. By the aid of this result we obtain some results stronger than Mazur’s theorem.

Asplund Functions and Projectional Resolutions of the Identity

*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

* Partially supported by Grant MM-428/94 of MESC.

Note on Radius Problems for Certain Class of Analytic Functions

MSC 2010: 30C45

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.