KNJ
is the category of compact normal joinfit frames and frame homomorphisms and
KReg
is the coreflective subcategory of compact regular frames. This work investigates
KNJ
through its interaction ...with
KReg
via the coreflection
ρ
. A
KNJ
morphism
ϕ
:
F
⟶
M
is
P
-essential if
ϕ
is skeletal and the map between the frames of polars,
P
(
ϕ
)
:
P
F
⟶
P
M
defined by
P
(
ϕ
)
(
p
)
=
ϕ
(
p
)
⊥
⊥
, is a boolean isomorphism. The
P
-essential morphisms in
KNJ
are closely related to the essential embeddings in
KReg
. We provide a characterization of the
P
-essential morphisms in
KNJ
and a connection to the essential embeddings in
KReg
. Further results about the preservation of joinfitness, the factorization of morphisms, and monomorphisms in
KNJ
are provided. Moreover, in the category of
KNJ
objects and skeletal frame homomorphisms,
KNJS
, we construct for
F
∈
KNJ
and
ϕ
:
ρ
F
⟶
H
(an arbitrary
KReg
essential embedding of
ρ
F
) the
KNJS
pushout of
ρ
F
:
ρ
F
⟶
F
and
ϕ
:
ρ
F
⟶
H
. Lastly, we investigate the epimorphisms and epicomplete objects in
KNJS
.
KReg
is the category of compact regular frames and frame homomorphisms. A class of
KReg
frames
H
is a hull class provided that: (i)
H
is closed under isomorphic copies; (ii) for every
F
∈
KReg
there ...exist an
h
F
∈
H
and a morphism
h
F
such that
F
≤
h
F
h
F
is essential; (iii) if
F
≤
ϕ
H
is essential and
H
∈
H
, then there exists
h
ϕ
:
h
F
⟶
H
for which
ϕ
=
h
ϕ
·
h
F
. This work provides techniques for identifying and generating hull classes in
KReg
. Moreover, for a compact regular frame
F
, we introduce and investigate various properties of projectability and disconnectivity of
F
and prove that for each property,
P
, the class of
KReg
-objects that satisfy
P
is a hull class in
KReg
. In addition, we provide examples of
KReg
hull classes that are not characterized by some form of projectability/disconnectivity and examples of classes of
KReg
-objects that are not hull classes.
W
denotes the category, or class of algebras, in the title. A hull operator (ho) in
W
is a function
ho
W
⟶
h
W
which can be called an essential closure operator. The family of these, denoted
ho
W
, ...is a proper class and a complete lattice in the ordering as functions “pointwise", with the bottom
Id
W
and top Conrad’s essential completion
e
. Other much studied hull operators are the divisible hull, maximum essential reflection, projectable hull, and Dedekind completion. This paper is the authors’ latest efforts to understand/create structure in
ho
W
through the nature of the interaction that an
h
might have with
B
, the bounded monocoreflection in
W
(e.g., Bh=hB). We define and investigate three functions
ho
W
⟶
ho
W
which stand in the relation
Id
W
≤
α
¯
(
h
)
≤
λ
¯
(
h
)
≤
c
¯
(
h
)
≤
h
.
General properties that an
h
might have, and particular choices of
h
, show various assignments of < and
=
in this chain.
Low flow (LF), defined as stroke volume index (SVi) <35 mL/m(2), prior to the procedure has been recently identified as a powerful independent predictor of early and late mortality in patients ...undergoing transcatheter aortic valve replacement (TAVR). The objectives of this study were to determine the evolution of SVi following TAVR and to assess the determinants and impact on mortality of early postprocedural SVi (EP-SVi).
We retrospectively analysed the clinical, Doppler echocardiographic and outcome data prospectively collected in 255 patients who underwent TAVR. Echocardiograms were performed before (baseline), within 5 days after procedure (early post procedure) and 6 months to 1 year following TAVR (late post procedure).
Patients with EP-SVi <35 mL/m(2) (n=138; 54%) had increased mortality (HR 1.97, p=0.003) compared with those with EP-SVi ≥35 mL/m(2) (n=117; 46%). Furthermore, patients with baseline SVi (B-SVi) <35 mL/m(2) and EP-SVI ≥35 mL/m(2), that is, normalised flow, had better survival (HR 0.46, p=0.03) than those with both B-SVi and EP-SVi <35 mL/m(2), that is, persistent LF, and similar survival compared with those with both B-SVi and EP-SVi ≥35 mL/m(2), that is, maintained normal flow. In a multivariable model analysis, EP-SVi was independently associated with increased risk of mortality (HR 1.41 per 10 mL/m(2) decrease, p=0.03). The preprocedural/intraprocedural factors associated with lower EP-SVi were lower B-SVi (standardised β β 0.36, p<0.001) atrial fibrillation (β -0.13, p=0.02) and transapical approach (β -0.22, p<0.001).
The measurement of EP-SVi is useful to assess the immediate haemodynamic benefit of TAVR and to predict the risk of late mortality.
The objective of the experiment was to classify 20 protein co-products and by-products of the biodiesel industry with potential to use in ruminant feeding. The meals evaluated were: cottonseed, ...canudo-de-pito, crambe, sunflower, castor-oil seeds detoxified with calcium, non-detoxified castor-oil seeds and soybean; and the cakes were: cottonseed, peanut, babassu, crambe, palm oil, sunflower, licuri, macauba seeds, non-detoxified castor-oil seeds, turnip and jatropha. The samples were quantified to determine dry matter (DM), organic matter (OM), crude protein (CP), ether extract (EE), neutral detergent fiber corrected for ash and protein (NDFap), non-fiber carbohydrates (NFC), acid detergent fiber corrected for ash and protein (ADFap), lignin, cutin and starch levels. The CP profile was characterized in fractions A, B1, B2, B3 and C. The in vitro dry matter digestibility (IVDMD), in vitro neutral detergent fiber digestibility (IVNDFD), rumen degradable and undegradable protein, intestinal digestibility, indigestible neutral detergent fiber and undegradable neutral detergent insoluble protein were evaluated. The OM, CP, EE, NDFap, NFC, ADFap, lignin, cutin and starch contents varied from 81.95 to 95.41%, 18.92 to 57.75%, 0.56 to 18.40%, 10.13 to 62.30%, 3.89 to 27.88%, 6.15 to 36.86%, 1.19 to 5.04%, 0 to 17.87% and 0.68 to 14.50%, respectively. The values of fractions A, B1, B2, B3 and C ranged from 5.40 to 43.31%, 0.08 to 37.63%, 16.75 to 79.39%, 1.86 to 59.15% and 0.60 to 11.47%, respectively. Concentrations of IVDMD, IVNDFD, rumen-degradable and undegradable protein, intestinal digestibility, indigestible NDF and undegradable neutral detergent insoluble protein ranged from 31.00 to 95.92%, 55.04 to 97.74%, 41.06 to 97.61%, 2.39 to 58.94, 9.27 to 94.26%, 1.05 to 40.80% and 0.29 to 2.92%, respectively. Some of these products can replace soybean meal, specially the Macauba seeds cake, cottonseed meal and peanut and turnip cakes based on digestive characteristics.
The category, or class of algebras, in the title is denoted by $\bf W$. A hull operator (ho) in $\bf W$ is a reflection in the category consisting of $\bf W$ objects with only essential embeddings as ...morphisms. The proper class of all of these is $\bf hoW$. The bounded monocoreflection in $\bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function $w: {\bf hoW} \longrightarrow {\bf W}^{\bf W}$ obtained as a finite composition of $B$ and $x$ a variable ranging in $\bf hoW$. The set of these,``Word'', is in a natural way a partially ordered semigroup of size $6$, order isomorphic to ${\rm F}(2)$, the free $0-1$ distributive lattice on $2$ generators. Then, $\bf hoW$ is partitioned into $6$ disjoint pieces, by equations and inequations in words, and each piece is represented by a characteristic order-preserving quotient of Word ($\approx {\rm F}(2)$). Of the $6$: $1$ is of size $\geq 2$, $1$ is at least infinite, $2$ are each proper classes, and of these $4$, all quotients are chains; another $1$ is a proper class with unknown quotients; the remaining $1$ is not known to be nonempty and its quotients would not be chains.
W
∞
denotes the category of archimedean
ℓ
-groups with designated weak unit and complete
ℓ
-homomorphisms that preserve the weak unit.
CmpT
2,∞
denotes the category of compact Hausdorff spaces with ...continuous skeletal maps. This work introduces the concept of a functorial polar function on
W
∞
and its dual a functorial covering function on
CmpT
2,∞
.
We demonstrate that functorial polar functions give rise to reflective hull classes in
W
∞
and that functorial covering functions give rise to coreflective covering classes in
CmpT
2,∞
. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal
α
, the class of
α
-projectable
ℓ
-groups is reflective in
W
∞
, and the class of
α
-disconnected compact Hausdorff spaces is coreflective in
CmpT
2,∞
. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).
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