scholarly journals Local complex dimensions of a fractal string

2012 ◽  
Vol 3 (4) ◽  
pp. 281
Author(s):  
Jacques Lévy Véhel ◽  
Franklin Mendivil
Keyword(s):  
Complex Dimensions ◽  
Local Complex ◽  
Fractal String

scholarly journals Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings

2018 ◽  
Vol 2 (4) ◽  
pp. 26 ◽  
Author(s):  
Michel Lapidus ◽  
Hùng Lũ’ ◽  
Machiel Frankenhuijsen
Keyword(s):  
Counting Function ◽  
Minkowski Dimension ◽  
Volume Formula ◽  
Fractal Strings ◽  
Complex Dimensions ◽  
Abscissa Of Convergence ◽  
Tubular Neighborhoods ◽  
Fractal String ◽  
Tube Formulas ◽  
Asymptotic Growth Rate

The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a p-adic fractal string L p , expressed in terms of the underlying complex dimensions. The general fractal tube formula obtained in this paper is illustrated by several examples, including the nonarchimedean Cantor and Euler strings. Moreover, we show that the Minkowski dimension of a p-adic fractal string coincides with the abscissa of convergence of the geometric zeta function associated with the string, as well as with the asymptotic growth rate of the corresponding geometric counting function. The proof of this new result can be applied to both real and p-adic fractal strings and hence, yields a unifying explanation of a key result in the theory of complex dimensions for fractal strings, even in the archimedean (or real) case.

scholarly journals Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 591
Author(s):  
Michel L. Lapidus ◽  
Machiel van Frankenhuijsen ◽  
Edward K. Voskanian
Keyword(s):  
Approximation Algorithm ◽  
Continued Fraction ◽  
Practical Method ◽  
Lll Algorithm ◽  
Fractal Strings ◽  
Complex Dimensions ◽  
Diophantine Approximations ◽  
Self Similar ◽  
Simultaneous Diophantine Approximations ◽  
Fractal String

The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self-similar fractal string. The implication of this procedure is that the set of complex dimensions of a nonlattice string has a quasiperiodic pattern. Using the LSA algorithm, together with the multiprecision polynomial solver MPSolve which is due to D. A. Bini, G. Fiorentino and L. Robol, we give a new and significantly more powerful presentation of the quasiperiodic patterns of the sets of complex dimensions of nonlattice self-similar fractal strings. The implementation of this algorithm requires a practical method for generating simultaneous Diophantine approximations, which in some cases we can accomplish by the continued fraction process. Otherwise, as was suggested by Lapidus and van Frankenhuijsen, we use the LLL algorithm of A. K. Lenstra, H. W. Lenstra, and L. Lovász.

scholarly journals Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140240 ◽  
Author(s):  
Michel L. Lapidus
Keyword(s):  
Riemann Hypothesis ◽  
Spectral Operator ◽  
Joint Work ◽  
Fractal Strings ◽  
Complex Dimensions ◽  
The Family ◽  
Expository Article ◽  
Riemann Zeta ◽  
Fractal String ◽  
The Right

This research expository article not only contains a survey of earlier work but also contains a main new result, which we first describe. Given c ≥0, the spectral operator can be thought of intuitively as the operator which sends the geometry onto the spectrum of a fractal string of dimension not exceeding c . Rigorously, it turns out to coincide with a suitable quantization of the Riemann zeta function ζ = ζ ( s ): , where ∂=∂ c is the infinitesimal shift of the real line acting on the weighted Hilbert space . In this paper, we establish a new asymmetric criterion for the Riemann hypothesis (RH), expressed in terms of the invertibility of the spectral operator for all values of the dimension parameter (i.e. for all c in the left half of the critical interval (0,1)). This corresponds (conditionally) to a mathematical (and perhaps also, physical) ‘phase transition’ occurring in the midfractal case when . Both the universality and the non-universality of ζ = ζ ( s ) in the right (resp., left) critical strip (resp., ) play a key role in this context. These new results are presented here. We also briefly discuss earlier joint work on the complex dimensions of fractal strings, and we survey earlier related work of the author with Maier and with Herichi, respectively, in which were established symmetric criteria for the RH, expressed, respectively, in terms of a family of natural inverse spectral problems for fractal strings of Minkowski dimension D ∈(0,1), with , and of the quasi-invertibility of the family of spectral operators (with ).

PENDIDIKAN UNTUK PEMBANGUNAN BERKELANJUTAN

2018 ◽  
Vol 10 (3) ◽  
pp. 304
Author(s):  
Familia Novita Simanjuntak
Keyword(s):  
Sustainable Development ◽  
Global Economy ◽  
Autonomous Motivation ◽  
Human Society ◽  
Environmental Attitude ◽  
Development Education ◽  
Environmental Behaviors ◽  
Sustainable Environment ◽  
Complex Dimensions ◽  
Earth Environment

ABSTRACTSustainable development urges to merge the three complex dimensions: global economy, global society and physically earth environment. Sachs (2015) states that sustainable development is the expert effort to comprehend the world and the method to solve the crowded earth issues by the global population growth that nine times increase than the first industry era. Education is one of fatal element for sustainable development phase especially for the human (society) development. Human development becomes the main core of invesment for economy development because it is prepared for the youngst as the next generation to develop economic improvement individually for their family and also for their community (include for the State’s development interest). Marshall, Hine and East (2017) studied about the education which develop the autonomous motivation to support individu execute the pro-environmental behaviors (PEBs). This autonomous motivation will establish the environmental attitude and personality in decision making and action of sustainable environment protection and preservation.Keywords: sustainable development, education, pro-environmental behaviors ABSTRAKPembangunan berkelanjutan berupaya untuk mengkaitkan tiga sistem yang rumit yaitu sistem ekonomi dunia, sistem sosial dunia dan lingkungan fisik bumi. Sachs (2015) menyatakan bahwa pembangunan berkelanjutan menjadi cara para pakar untuk memahami dunia dan sebuah metode untuk menyelesaikan permasalahan dunia yang berawal dari sesaknya bumi akibat pertumbuhan penduduk dunia yang sudah mencapai sembilan kali lebih banyak dari populasi manusia yang hidup pada jaman dimulainya revolusi industri. Pendidikan adalah salah satu komponen yang penting dalam proses pembangunan berkelanjutan terutama pembangunan yang terkait manusia (sosial). Pembangunan manusia menjadi bagian vital dari investasi yang dibutuhkan dalam pembangunan ekonomi karena merupakan jalur investasi yang disiapkan untuk anak-anak sebagai generasi penerus yang akan melanjutkan perbaikan ekonomi baik secara individu bagi keluarganya maupun secara berkelompok bagi komunitasnya (termasuk kepentingan pembangunan di Negaranya). Penelitian Marshall, Hine and East (2017) menyatakan bahwa pendidikan dapat membentuk dorongan dari dalam setiap individu untuk melakukan perilaku pro lingkungan hidup (pro-environmental behaviours). Dorongan dari dalam individu ini secara otonomi membentuk watak dan karakter yang ramah lingkungan untuk membuat keputusan dan bertindak yang melindungi dan menjaga keberlanjutan lingkungan hidup.Kata kunci: pembangunan berkelanjutan, pendidikan, pro-environmental beharviors

Perfection Makes Practice

2006 ◽  
Vol 23 (3) ◽  
pp. 98-100
Author(s):  
Muhamad Ali
Keyword(s):  
Social Relations ◽  
Muslim Community ◽  
Beliefs And Practices ◽  
Psychological Dimension ◽  
South Sulawesi ◽  
Complex Dimensions ◽  
History Of Religions ◽  
History Of

Studies of Islam in Southeast Asia have sought to better understand its multifacetedand complex dimensions, although one may make a generalizedcategorization of Muslim beliefs and practices based on a fundamental differencein ideologies and strategies, such as cultural and political Islam.Anna M. Gade’s Perfection Makes Practice stresses the cultural aspect ofIndonesian Muslim practices by analyzing the practices of reciting andmemorizing the Qur’an, as well as the annual competition.Muslim engagement with the Qur’an has tended to emphasize the cognitiveover the psychological dimension. Perfection Makes Practice analyzesthe role of emotion in these undertakings through a combination ofapproaches, particularly the history of religions, ethnography, psychology,and anthropology. By investigating Qur’anic practitioners in Makassar,South Sulawesi, during the 1990s, Gade argues that the perfection of theQur’an as a perceived, learned, and performed text has made and remade thepractitioners, as well as other members of the Muslim community, to renewor increase their engagement with the holy text. In this process, she suggests,moods and motivation are crucial to preserving the recited Qur’an and revitalizingthe Muslim community.In chapter 1, Gade begins with a theoretical consideration for her casestudy. Drawing from concepts that emphasize the importance of feeling andemotion in ritual and religious experience, she develops a conceptualizationof this engagement. In chapter 2, Gade explains memorization within thecontext of the self and social relations. She argues that Qur’anic memorizershave a special relationship with its style and structure, as well as with thesocial milieu. Although Qur’anic memorization is a normal practice for mostMuslims, its practitioners have learned how to memorize and recite beautifullysome or all of the Qur’an’s verses, a process that requires emotion ...

Development of an unmanned tractor chassis for precision farming

2020 ◽  
pp. 47-53
Author(s):  
YU.V. Galyishev ◽  
R.Yu. Dobretsov ◽  
G.P. Porshnev ◽  
E.G. Saharova ◽  
D.V. Uvakina ◽  
...  
Keyword(s):  
Precision Farming ◽  
Autonomous Control ◽  
Kinematic Scheme ◽  
Local Complex ◽  
Friction Clutch

The development of the chassis of an unmanned tractor for a local complex of precision fanning is considered. The design is based on the kinematic scheme of the shaft gearbox, which implements a large number of modes and the principle of two-line transmission. A feature of this scheme is the presence of parallel load shafts. Keywords: wheeled tractor, autonomous control, two-line transmission, slipping, disc friction clutch. [email protected]

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

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