scholarly journals Convolution operators of weak type $(2,\,2)$ which are not of strong type $(2,\,2)$

1983 ◽  
Vol 87 (4) ◽  
pp. 695-695
Author(s):  
Ryszard Szwarc
Keyword(s):  
Weak Type ◽  
Strong Type ◽  
Convolution Operators

scholarly journals Strong and weak (1, 2, 3) homotopies on knot projections

2015 ◽  
Vol 26 (09) ◽  
pp. 1550069 ◽  
Author(s):  
Noboru Ito ◽  
Yusuke Takimura
Keyword(s):  
Weak Type ◽  
Equivalence Classes ◽  
Dimensional Sphere ◽  
Strong Type ◽  
Homotopy Equivalence ◽  
Reidemeister Moves ◽  
Generic Immersion ◽  
Type 3

A knot projection is an image of a generic immersion from a circle into a two-dimensional sphere. We can find homotopies between any two knot projections by local replacements of knot projections of three types, called Reidemeister moves. This paper defines an equivalence relation for knot projections called weak (1, 2, 3) homotopy, which consists of Reidemeister moves of type 1, weak type 2, and weak type 3. This paper defines the first nontrivial invariant under weak (1, 2, 3) homotopy. We use this invariant to show that there exist an infinite number of weak (1, 2, 3) homotopy equivalence classes of knot projections. By contrast, all equivalence classes of knot projections consisting of the other variants of a triple type, i.e. Reidemeister moves of (1, strong type 2, strong type 3), (1, weak type 2, strong type 3), and (1, strong type 2, weak type 3), are contractible.

scholarly journals INFLUENCE OF THE TYPE OF NERVOUS ACTIVITY ON THE MILK PRODUCTION OF COWS

2020 ◽  
Author(s):  
Lina Karlova ◽  
◽  
Olena Lesnovska ◽  
Roman Mylostyvyi ◽  
◽  
...  
Keyword(s):  
Nervous System ◽  
Milk Yield ◽  
Weak Type ◽  
Nervous Activity ◽  
Fat Content ◽  
Strong Type ◽  
The Difference ◽  
Productive Traits ◽  
Relative Decline ◽  
Morning Milk

The aim of the research was to evaluate the influence of the type of the nervous system on the productive and reproductive qualities of animals. The type of nervous system (strong, weak) of cows of the Ukrainian red dairy breed was determined by the index of the nervous system, which is based on the variability of the fat content in the morning milk yield after changing the conditions of cows keeping. Under the new conditions of keeping cows with a strong type of nervous activity, the coefficients of variability of the morning milk yield and the fat content in milk practically remained at the same level (their slight increase was noted at the level of 4.5 and 3.1%). In cows of a weak type under similar conditions of keeping, a significant increase in the variability of milk yield (by 53.6%) and fat content in milk (by 266.7%) was found. In animals of both types, in the first days of summer-camp keeping, in comparison with winter-stall keeping, there was an increase in milk yield and a decrease in fat content in milk. In cows of the strong type, the fat content decreased by 0.08% and of the weak type by 0.12%. The average index of the nervous system type in animals of the strong type is 1.18, and in cows of the weak type 2.71 (P> 0.999). Before and during milking, the pulse rate in the cows of weak type was higher by 8.0 and 10.8 beats / min. (P> 0.999), compared with the strong type. The animals of strong type of the nervous system, in comparison with the weak type, had a smaller thickness of the concha and skin, a higher pulse and respiratory rate, and a lower rectal body temperature. In cows of a strong type of the nervous system in postnatal ontogenesis, the formation of productive traits took place more rapidly and they better adapted to the conditions of the external environment. This is evidenced by their high coefficient of relative decline in the growth at the age of one (85.0) than in animals with a weak type of nervous system (78.5). The advantage of cows with a strong type of nervous activity over a weak one in milk yield was 348 kg (P>0.95) and in milk fat 8.0 kg. The service period in animals with a strong type of nervous activity was 6.3 days shorter. The animals with a strong type of nervous activity during the first lactation had a higher adaptation index compared with animals of a weak type. The difference for this indicator is 0.49 (or 3.7%). They also had a higher productivity index for the first (3.1%) and second (4.0%) lactation. Thus, the typological features of the nervous activity of cows affect the formation of the most important functions of the body, which can be used in breeding work to improve the herd.

Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)

1995 ◽  
Vol 47 (2) ◽  
pp. 225-245
Author(s):  
Nakhlé Asmar ◽  
Earl Berkson ◽  
T. A. Gillespie
Keyword(s):  
Abelian Group ◽  
Weak Type ◽  
Full Range ◽  
Locally Compact Abelian Group ◽  
Strong Type ◽  
Locally Compact ◽  
Linearization Methods ◽  
Maximal Theorem ◽  
Abstract Setting ◽  
Central Result

AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

scholarly journals A note on weighted maximal inequalities

1997 ◽  
Vol 40 (1) ◽  
pp. 193-205
Author(s):  
Qinsheng Lai
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Strong Type ◽  
Maximal Inequalities ◽  
Littlewood Maximal Operator

In this paper, we obtain some characterizations for the weighted weak type (1, q) inequality to hold for the Hardy-Littlewood maximal operator in the case 0<q<1; prove that there is no nontrivial weight satisfying one-weight weak type (p, q) inequalities when 0<p≠q< ∞, and discuss the equivalence between the weak type (p, q) inequality and the strong type (p, q) inequality when p≠q.

scholarly journals Strong Type 1, but Impaired Type 2, Immune Responses Contribute to Orientia tsutsugamushi-Induced Pathology in Mice

2014 ◽  
Vol 8 (9) ◽  
pp. e3191 ◽  
Author(s):  
Lynn Soong ◽  
Hui Wang ◽  
Thomas R. Shelite ◽  
Yuejin Liang ◽  
Nicole L. Mendell ◽  
...  
Keyword(s):  
Immune Responses ◽  
Strong Type ◽  
Orientia Tsutsugamushi

scholarly journals Maximal operators for the holomorphic Laguerre semigroup

2005 ◽  
Vol 97 (2) ◽  
pp. 235 ◽  
Author(s):  
Emanuela Sasso
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Maximal Operators ◽  
Strong Type ◽  
Half Integer ◽  
Starting Point

For each $p$ in $[1,\infty)$ let $\mathbf{E}_p$ denote the closure of the region of holomorphy of the Laguerre semigroup $\{M^{\alpha}_t:t>0\}$ on $L^p$ with respect to the Laguerre measure $\mu_{\alpha}$. We prove weak type and strong type estimates for the maximal operator $f\mapsto \sup\{|M^{\alpha}_z f|:z\in \mathbf{E}_p\}$. In particular, we give a new proof for the weak type $1$ estimate for the maximal operator associated to $M^{\alpha}_t$. Our starting point is the well-known relationship between the Laguerre semigroup of half-integer parameter and the Ornstein-Uhlenbeck semigroup.

Sign in / Sign up

Export Citation Format

Share Document