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Search Results: 1 - 10 of 33361 matches for " Machiel van Frankenhuysen "
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A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation
Michel Lapidus,Machiel van Frankenhuysen
Mathematics , 2001,
Abstract: Assuming some regularity of the dynamical zeta function, we establish an explicit formula with an error term for the prime orbit counting function of a suspended flow. We define the subclass of self-similar flows, for which we give an extensive analysis of the error term in the corresponding prime orbit theorem.
The ABC Theorem for Meromorphic Functions
Machiel van Frankenhuijsen
Mathematics , 2008,
Abstract: Using a `height-to-radical' identity, we define the archimedean contribution to the radical, $r_\arch$, and we give a new proof of the abc theorem for the field of meromorphic functions. The first step of the proof is completely formal and yields that the height is bounded by the radical, $h\leq r$, where $r=r_\na+r_\arch$ is the radical completed with the archimedean contribution. The second step is analytic in nature and uses the lemma on the logarithmic derivative to derive a bound for $r_\arch$.
The Riemann Hypothesis for Function Fields over a Finite Field
Machiel van Frankenhuijsen
Mathematics , 2008,
Abstract: We discuss Enrico Bombieri's proof of the Riemann hypothesis for curves over a finite field. Reformulated, it states that the number of points on a curve $\C$ defined over the finite field $\F_q$ is of the order $q+O(\sqrt{q})$. The first proof was given by Andr\'e Weil in 1942. This proof uses the intersection of divisors on $\C\times\C$, making the application to the original Riemann hypothesis so far unsuccessful, because $\spec\Z\times\spec\Z=\spec\Z$ is one-dimensional. A new method of proof was found in 1969 by S. A. Stepanov. This method was greatly simplified and generalized by Bombieri in 1973. Bombieri's method uses functions on $\C\times\C$, again precluding a direct translation to a proof of the original Riemann hypothesis. However, the two coordinates on $\C\times\C$ have different roles, one coordinate playing the geometric role of the variable of a polynomial, and the other coordinate the arithmetic role of the coefficients of this polynomial. The Frobenius automorphism of $\C$ acts on the geometric coordinate of $\C\times\C$. In the last section, we make some suggestions how Nevanlinna theory could provide a model of $\spec\Z\times\spec\Z$ that is two-dimensional and carries an action of Frobenius on the geometric coordinate.
Phase transitions on Hecke C*-algebras and class-field theory over Q
Marcelo Laca,Machiel van Frankenhuijsen
Mathematics , 2004,
Abstract: We associate a canonical Hecke pair of semidirect product groups to the ring inclusion of the algebraic integers $\oo$ in a number field $\kk$, and we construct a C*-dynamical system on the corresponding Hecke C*-algebra, analogous to the one constructed by Bost and Connes for the inclusion of the integers in the rational numbers. We describe the structure of the resulting Hecke C*-algebra as a semigroup crossed product and then, in the case of class number one, analyze the equilibrium (KMS) states of the dynamical system. The extreme KMS$_\beta$ states at low-temperature exhibit a phase transition with symmetry breaking that strongly suggests a connection with class field theory. Indeed, for purely imaginary fields of class number one, the group of symmetries, which acts freely and transitively on the extreme KMS$_\infty$ states, is isomorphic to the Galois group of the maximal abelian extension over the field. However, the Galois action on the restrictions of extreme KMS$_\infty$ states to the (arithmetic) Hecke algebra over $\kk$, as given by class-field theory, corresponds to the action of the symmetry group if and only if the number field $\kk$ is $\Q$.
Fractality, Self-Similarity and Complex Dimensions
Michel L. Lapidus,Machiel van Frankenhuijsen
Mathematics , 2004,
Abstract: We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several strands to discuss a possible approach to establishing a cohomological interpretation of the complex dimensions.
An osseous lesion in a 10-year-old boy with Hodgkin's lymphoma: a case report
Machiel van den Akker, Vadiem Zudekov, Asher Moser, Joseph Kapelushnik
Journal of Medical Case Reports , 2011, DOI: 10.1186/1752-1947-5-511
Abstract: We report the case of a 10-year-old Caucasian boy who presented to our facility with a bony lesion of the right clavicle and enlarged cervical lymph nodes. A simultaneous biopsy of the lymph node and of the osteolytic process of his right proximal clavicle was performed and revealed two different kinds of lesions: a mixed cellularity Hodgkin's lymphoma and an osteochondroma.Since the latter is a common benign bone tumor, which should not interfere with the staging of the lymphoma, we emphasize the importance of ensuring that all efforts are made to acquire a diagnostic biopsy of all atypical lesions.Lymphoma is the third most common childhood malignancy following leukemia and brain tumors, accounting for approximately 12% of childhood cancers. Two-thirds of lymphomas diagnosed in children are non-Hodgkin's lymphomas (NHL), with the remainder being Hodgkin's lymphomas (HL). Anatomic extent of disease and tumor burden at presentation are significant factors determining choice of therapy and prognosis. HL typically involves the lymphatic system, and is usually supra-diaphragmatic. HL often follows a pattern of contiguous spread from one nodal group to the next anatomical region. Extra-nodal involvement is more common in NHL. Extra-nodal invasion of adjacent tissues is seen in up to 15% of cases and hematogenous spread in up to 10% of newly diagnosed cases. Osseous localizations have been described in 10% to 20% of cases of relapsed or refractory HL, but less than 2% at the time of initial presentation. Here, we describe a case of an osteochondroma (OC) in a child with Hodgkin's disease not affecting therapy or prognosis.Due to enlarged lymph nodes in his right neck region, a 10-year-old Caucasian boy underwent ultrasonic investigation and was treated with a short course of antibiotics 18 months prior to his presentation at our facility. Two months before his current admission, our patient reported local pain and enlargement of the same area in the neck. No B symptoms w
Minkowski Measurability and Exact Fractal Tube Formulas for p-Adic Self-Similar Strings
Michel L. Lapidus,Lu Hung,Machiel van Frankenhuijsen
Mathematics , 2012,
Abstract: The theory of p-adic fractal strings and their complex dimensions was developed by the first two authors in [17, 18, 19], particularly in the self-similar case, in parallel with its archimedean (or real) counterpart developed by the first and third author in [28]. Using the fractal tube formula obtained by the authors for p-adic fractal strings in [20], we present here an exact volume formula for the tubular neighborhood of a p-adic self-similar fractal string Lp, expressed in terms of the underlying complex dimensions. The periodic structure of the complex dimensions allows one to obtain a very concrete form for the resulting fractal tube formula. Moreover, we derive and use a truncated version of this fractal tube formula in order to show that Lp is not Minkowski measurable and obtain an explicit expression for its average Minkowski content. The general theory is illustrated by two simple examples, the 3-adic Cantor string and the 2-adic Fibonacci strings, which are nonarchimedean analogs (introduced in [17, 18]) of the real Cantor and Fibonacci strings studied in [28].
The Political Frontiers of Europe as a Civil Society: J. Habermas' Rejection of a European Volk and M. Foucault's Balance of Power as Protections Against European Nation-State
Machiel Karskens
Limes. Cultural Regionalistics , 2008, DOI: 10.3846/2029-0187.2008.1.186-198
Abstract: With the help of J. Habermas and M. Foucault, it is argued that the idea of Europe is, first of all, the ideal of an unlimited civil society. Human rights, the rule of law and the legal European institutions are its political backbone. The European Union itself is somehow the realization of this ideal conception of a borderless, unlimited society. It is argued that the European Union in this respect is a heterotopia within the bordered and sovereign member states themselves. Seen from the outside, however, and in the world of geopolitics, Europe is a political power with closed borders and excluding frontiers. In this respect the European Union is a continuation of the old European Balance of Power.
The Dutch version of the Oral Health Impact Profile (OHIP-NL): Translation, reliability and construct validity
Marylee J van der Meulen, Mike T John, Machiel Naeije, Frank Lobbezoo
BMC Oral Health , 2008, DOI: 10.1186/1472-6831-8-11
Abstract: The original English version of the OHIP was translated into the Dutch language, following the guidelines for cross-cultural adaptation of health-related quality of life measures. The resulting OHIP-NL's psychometric properties were examined in a sample of 119 patients (68.9 % women; mean age = 57.1 ± 12.2 yrs). They were referred to the clinic of Prosthodontics and Implantology with complaints concerning their partial or full dentures or other problems with missing teeth. To establish the reliability of the OHIP-NL, internal consistency and test-retest reliability (N = 41; 1 – 2 weeks interval) were examined, using Cronbach's alpha and intraclass correlation coefficients (ICC), respectively. Further, construct validity was established by calculating ANOVA.Internal consistency and test-retest reliability were excellent (Cronbach's alpha = 0.82 – 0.97; ICC = 0.78 – 0.90). In addition, all associations were significant and in the expected direction.In conclusion: the OHIP-NL can be considered a reliable and valid instrument to measure oral health-related quality of life.Since the recognition of the multidimensional character of health issues, a conceptual framework has been created to analyze the role of psychosocial factors in health and disease [1]. In order to study the role of such factors in dentistry, Reisine et al. [2] examined dental patients with the use of a general health-related quality of life measure, the Sickness Impact Profile. Specific instruments to measure the impact of oral disease on the quality of life of individuals were developed as well, like the Social Impact of Dental Disease [3] and the Dental Impact Profile [4]. Likewise, Slade & Spencer [5] published a study on the development and evaluation of the Oral Health Impact Profile (OHIP), in which the guidelines of the World Health Organization [6], to distinguish more systematically between functional limitation and social impact of physical problems, were followed. This instrument consists of
Physiological and neurophysiological determinants of postcancer fatigue: design of a randomized controlled trial
Hetty Prinsen, Gijs Bleijenberg, Machiel J. Zwarts, Maria T.E. Hopman, Arend Heerschap, Hanneke W.M. van Laarhoven
BMC Cancer , 2012, DOI: 10.1186/1471-2407-12-256
Abstract: Fifty seven severely fatigued and 21 non-fatigued cancer survivors will be recruited from the Radboud University Nijmegen Medical Centre. Participants should have completed treatment of a malignant, solid tumour minimal one year earlier and should have no evidence of disease recurrence. Severely fatigued patients are randomly assigned to either the intervention condition (cognitive behaviour therapy) or the waiting list condition (start cognitive behaviour therapy after 6?months). All participants are assessed at baseline and the severely fatigued patients also after 6?months follow-up (at the end of cognitive behaviour therapy or waiting list). Primary outcome measures are fatigue severity, central and peripheral fatigue, brain morphology and function, and physical condition and activity.This study will be the first randomized controlled trial that characterizes (neuro)physiological factors of fatigue in disease-free cancer survivors and evaluates to which extent these factors can be influenced by cognitive behaviour therapy. The results of this study are not only essential for a theoretical understanding of this invalidating condition, but also for providing an objective biological marker for fatigue that could support the diagnosis and follow-up of treatment.The study is registered at http://ClinicalTrials.gov webcite (NCT01096641).
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