scholarly journals Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator

2019 ◽  
Vol 149 (6) ◽  
pp. 1577-1594
Author(s):  
Clifford Gilmore ◽  
Eero Saksman ◽  
Hans-Olav Tylli
Keyword(s):  
Growth Rate ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Optimal Growth ◽  
Differentiation Operator ◽  
Minimal Growth ◽  
Partial Differentiation

AbstractWe solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on ℝN, that is frequently hypercyclic with respect to the partial differentiation operator ∂/∂xk and which has a minimal growth rate in terms of the average L2-norm on spheres of radius r > 0 as r → ∞.

Mean Growth of Harmonic Functions of Beurling Type

1984 ◽  
Vol 27 (4) ◽  
pp. 405-409
Author(s):  
Manning G. Collier ◽  
John A. Kelingos
Keyword(s):  
Growth Rate ◽  
Harmonic Function ◽  
General Result ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Concave Function ◽  
Taylor Coefficients

AbstractA harmonic function on the unit disc is of Beurling type ω if its Fourier (or Taylor) coefficients grow no faster than exp ω(|n|) as |n|→∞, where ω is a given increasing, concave function with ω(x)/x ↓ 0 as x → ∞. These harmonic functions are characterized by the growth rate of their L1-norms on circles of radius r as r → 1. The classical Schwartz result follows as a corollary by taking ω(x) = log(1+x). The Gevrey case is also included in the general result if one uses ω(x) = xα, 0 < α < 1.

Rate of growth of frequently hypercyclic functions

2010 ◽  
Vol 53 (1) ◽  
pp. 39-59 ◽  
Author(s):  
O. Blasco ◽  
A. Bonilla ◽  
K.-G. Grosse-Erdmann
Keyword(s):  
Harmonic Functions ◽  
Entire Functions ◽  
Translation Operator ◽  
Differentiation Operator ◽  
Partial Differentiation ◽  
Rate Of Growth ◽  
Growth Of Entire Functions

AbstractWe study the rate of growth of entire functions that are frequently hypercyclic for the differentiation operator or the translation operator. Moreover, we prove the existence of frequently hypercyclic harmonic functions for the translation operator and we study the rate of growth of harmonic functions that are frequently hypercyclic for partial differentiation operators.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals 261 Increasing dietary amylose reduces rate of starch digestion and increases microbial fermentation in weaned pigs

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 86-86
Author(s):  
F P Y Tan ◽  
L F Wang ◽  
E Beltranena ◽  
R T Zijlstra
Keyword(s):  
Growth Rate ◽  
Block Design ◽  
Optimal Growth ◽  
Metabolite Profile ◽  
Proximal Colon ◽  
Starch Digestion ◽  
Gut Health ◽  
Weaned Pigs ◽  
Ileal Digestibility ◽  
Beneficial Effects

Abstract Beneficial effects of SCFA in modulating gut health stimulated interest on dietary strategies to increase intestinal microbial activity and digesta SCFA. Amylose has lower apparent ileal digestibility (AID) than amylopectin. In the large intestine, undigested starch is fermented by microbes producing SCFA. The objective was to determine effects of increasing dietary amylose on starch flow and metabolite profile along the intestinal tract in weaned pigs. Weaned pigs (n=32; initial BW, 8.4 kg) were randomly allocated to 4 diets containing 67% starch with 0, 20, 35, or 70% amylose in a randomized complete block design. On day 21, pigs were euthanized to collect digesta and feces for evaluating starch digestion and metabolite profiles. Apparent hindgut fermentation (AHF) was calculated as apparent total tract digestibility minus AID. Feed intake was 12% lower (P &lt; 0.05) and growth rate was 18% lower (P &lt; 0.05) for pigs fed 70% amylose than pigs fed 0, 20, or 35% amylose. Feed efficiency was greatest (P &lt; 0.05) for pigs fed with 35% amylose. The AID of starch was 44% lower (P &lt; 0.05) in pigs fed 70% amylose. Starch was completely digested by the proximal colon in pigs fed 0, 20, or 35% amylose, but AHF of starch was 14% greater (P &lt; 0.05) in pigs fed 70% amylose. Increasing dietary amylose did not alter digesta SCFA in the small intestine, but increased (P &lt; 0.05) digesta SCFA in the cecum, specifically acetate and total SCFA, and increased (P &lt; 0.05) propionate and valerate in all sections of the colon. In conclusion, increasing dietary amylose in weaned pigs stimulated hindgut fermentation of starch with a corresponding increase in digesta total SCFA in the cecum and colon. Optimizing dietary amylose may exert its effect as dietary prebiotic while promoting an optimal growth rate in young pigs.

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

scholarly journals UTILITY MAXIMIZATION IN A BINOMIAL MODEL WITH TRANSACTION COSTS: A DUALITY APPROACH BASED ON THE SHADOW PRICE PROCESS

2014 ◽  
Vol 17 (04) ◽  
pp. 1450022 ◽  
Author(s):  
CHRISTIAN BAYER ◽  
BEZIRGEN VELIYEV
Keyword(s):  
Growth Rate ◽  
Asymptotic Expansion ◽  
Transaction Costs ◽  
Continuous Time ◽  
Shadow Price ◽  
Optimal Growth ◽  
Order Effect ◽  
Explicit Construction ◽  
Binomial Model ◽  
Price Process

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be made explicit for small transaction costs (in the sense of an asymptotic expansion). Here we find that, contrary to the classical results in continuous time, see Janeček and Shreve (2004), Finance and Stochastics8, 181–206, the size of the no-trade-region as well as the asymptotic growth rate depend analytically on the level λ of transaction costs, implying a linear first-order effect of perturbations of (small) transaction costs, in contrast to effects of orders λ1/3 and λ2/3, respectively, as in continuous time models. Following the recent study by Gerhold et al. (2013), Finance and Stochastics17, 325–354, we obtain the asymptotic expansion by an almost explicit construction of the shadow price process.

scholarly journals The Minimal Growth Rate of Cocompact Coxeter Groups in Hyperbolic 3-space

2014 ◽  
Vol 66 (2) ◽  
pp. 354-372 ◽  
Author(s):  
Ruth Kellerhals ◽  
Alexander Kolpakov
Keyword(s):  
Growth Rate ◽  
Coxeter Group ◽  
Coxeter Groups ◽  
Triangle Group ◽  
Minimal Growth ◽  
Salem Number

AbstractDue to work of W. Parry it is known that the growth rate of a hyperbolic Coxeter group acting cocompactly on H3 is a Salem number. This being the arithmetic situation, we prove that the simplex group (3,5,3) has the smallest growth rate among all cocompact hyperbolic Coxeter groups, and that it is, as such, unique. Our approach provides a different proof for the analog situation in H2 where E. Hironaka identified Lehmer's number as the minimal growth rate among all cocompact planar hyperbolic Coxeter groups and showed that it is (uniquely) achieved by the Coxeter triangle group (3,7).

scholarly journals Some remarks concerning harmonic functions on homogeneous graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Anders Karlsson
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Cayley Graphs ◽  
Group Cohomology ◽  
Radial Variation ◽  
International Audience

International audience We obtain a new result concerning harmonic functions on infinite Cayley graphs $X$: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of $X$. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.

scholarly journals <sup>210</sup>Pb-<sup>226</sup>Ra chronology reveals rapid growth rate of <i>Madrepora oculata</I> and <i>Lophelia pertusa</i> on world's largest cold-water coral reef

2011 ◽  
Vol 8 (6) ◽  
pp. 12247-12283
Author(s):  
P. Sabatier ◽  
J.-L. Reyss ◽  
J. M. Hall-Spencer ◽  
C. Colin ◽  
N. Frank ◽  
...  
Keyword(s):  
Growth Rate ◽  
Coral Reef ◽  
Linear Growth ◽  
Cold Water ◽  
Optimal Growth ◽  
Growth Conditions ◽  
Age And Growth ◽  
Linear Growth Rate ◽  
Lophelia Pertusa ◽  
Water Coral

Abstract. Here we show the use of the 210Pb-226Ra excess method to determine the growth rate of corals from one of the world's largest known cold-water coral reef, the Røst Reef off Norway. Two large branching framework-forming cold-water coral specimens, one Lophelia pertusa and one Madrepora oculata were collected alive at 350 m water depth from the Røst Reef at ~67° N and ~9° E. Pb and Ra isotopes were measured along the major growth axis of both specimens using low level alpha and gamma spectrometry and the corals trace element compositions were studied using ICP-QMS. Due to the different chemical behaviors of Pb and Ra in the marine environment, 210Pb and 226Ra were not incorporated the same way into the aragonite skeleton of those two cold-water corals. Thus to assess of the growth rates of both specimens we have here taken in consideration the exponential decrease of initially incorporated 210Pb as well as the ingrowth of 210Pb from the decay of 226Ra. Moreover a~post-depositional 210Pb incorporation is found in relation to the Mn-Fe coatings that could not be entirely removed from the oldest parts of the skeletons. The 226Ra activities in both corals were fairly constant, then assuming constant uptake of 210Pb through time the 210Pb-226Ra chronology can be applied to calculate linear growth rate. The 45.5 cm long branch of M. oculata reveals an age of 31 yr and a~linear growth rate of 14.4 ± 1.1 mm yr−1, i.e. 2.6 polyps per year. However, a correction regarding a remaining post-depositional Mn-Fe oxide coating is needed for the base of the specimen. The corrected age tend to confirm the radiocarbon derived basal age of 40 yr (using 14C bomb peak) with a mean growth rate of 2 polyps yr−1. This rate is similar to the one obtained in Aquaria experiments under optimal growth conditions. For the 80 cm-long specimen of L. pertusa a remaining contamination of metal-oxides is observed for the middle and basal part of the coral skeleton, inhibiting similar accurate age and growth rate estimates. However, the youngest branch was free of Mn enrichment and this 15 cm section reveals a growth rate of 8 mm yr−1 (~1 polyp every two to three years). However, the 210Pb growth rate estimate is within the lowermost ranges of previous growth rate estimates and may thus reflect that the coral was not developing at optimal growth conditions. Overall, 210Pb-226Ra dating can be successfully applied to determine the age and growth rate of framework-forming cold-water corals, however, removal of post-depositional Mn-Fe oxide deposits is a prerequisite. If successful, large branching M. oculata and L. pertusa coral skeletons provide unique oceanographic archive for studies of intermediate water environmentals with an up to annual time resolution and spanning over many decades.

Growth Rate Model and Temperature-Changing Fermentation Process of Pseudomonas Syringae Pv. Mori M4-13

2011 ◽  
Vol 282-283 ◽  
pp. 531-534
Author(s):  
Yao Liang ◽  
Jie Cheng ◽  
Rong Bin Lv ◽  
Sheng Jie Zhang ◽  
Fei Pan ◽  
...  
Keyword(s):  
Growth Rate ◽  
Pseudomonas Syringae ◽  
Large Scale ◽  
Optimal Growth ◽  
Growth Substance ◽  
Plant Growth Substance ◽  
High Efficient ◽  
Root Model ◽  
Fermentation Pattern ◽  
Solid Foundation

Pseudomonas syringaepv. mori M4-13 is a new coronatine-production strain isolated from mulberry trees. As a high efficient plant growth substance, coronatine is difficult to obtain from the traditional bacteria under the high temperature. The fermentation temperature cannot be greater than 301K. However, the coronatine production is strictly growth associated. Therefore, biomass growth and accumulation of coronatine should be studied coordinately. In this paper, the growth rate of the strain was studied by the square root model, and the temperature-changing fermentation pattern of coronatine was optimized. In the fitting function of , the value of b was 0.03276, c was 0.1759, R2= 0.99. Based on the results, the optimal growth temperature of Pseudomonas syringae pv.moriM4-13 is 305K. The accumulation of coronatine reaches the peak, when the strain was incubated at the 305K for 3 days, following with the fermentation at 291K for another 3days. This fermentation pattern lay a solid foundation for the large-scale applications in the industrial production.

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