We investigate value distribution and uniqueness problems of difference polynomials of meromorphic functions. In particular, we show that for a finite order transcendental meromorphic function
f with
...λ
(
1
/
f
)
<
ρ
(
f
)
and a non-zero complex constant
c, if
n
⩾
2
, then
f
(
z
)
n
f
(
z
+
c
)
assumes every non-zero value
a
∈
C
infinitely often. This research also shows that there exist two sets
S
1
with 9 (resp. 5) elements and
S
2
with 1 element, such that for a finite order nonconstant meromorphic (resp. entire) function
f and a non-zero complex constant
c,
E
f
(
z
)
(
S
j
)
=
E
f
(
z
+
c
)
(
S
j
)
(
j
=
1
,
2
)
imply
f
(
z
)
≡
f
(
z
+
c
)
. This gives an answer to a question of Gross concerning a finite order meromorphic function
f and its shift.
In this paper, we investigate the relation of the Nevanlinna characteristic functions
T
(
r
,
f
(
q
z
)
)
and
T
(
r
,
f
(
z
)
)
for a zero-order meromorphic function
f and a non-zero constant
q. It ...is shown that
T
(
r
,
f
(
q
z
)
)
=
(
1
+
o
(
1
)
)
T
(
r
,
f
(
z
)
)
for all
r on a set of lower logarithmic density 1. This estimate is sharp in the sense that for any
q
∈
C
such that
|
q
|
≠
1
, and
ρ
>
0
, there exists a meromorphic function
h of order
ρ such that
T
(
r
,
h
(
q
z
)
)
=
(
|
q
|
ρ
+
o
(
1
)
)
T
(
r
,
h
(
z
)
)
as
r
→
∞
outside of an exceptional set of finite linear measure. As applications, we give some results on zero-order meromorphic solutions of
q-difference equations, and on value distribution and uniqueness of certain types of
q-difference polynomials.
The concerted elimination reaction class of peroxyl-hydroperoxyl alkyl radicals (•OOQOOH) plays a crucial role in the low-temperature combustion of normal-alkyl cyclohexanes. The generation of the ...relatively unreactive HO2 radicals in this reaction is one of the factors leading to the negative temperature coefficient (NTC) behavior, which hinders the low-temperature oxidation of normal-alkyl cyclohexanes. In this study, 44 reactions are selected and divided into 4 different subclasses according to the nature of the carbon atom where the H atom is eliminated and the reaction center position. Utilizing the CBS-QB3 method, we compute the energy barriers for the concerted elimination reactions of peroxyl-hydroperoxyl alkyl radicals. Following this, we assess both the high-pressure limit and pressure-dependent rate constants for all reactions by applying TST and RRKM/ME theory. These calculations allow for the development of rate rules, which come to fruition through an averaging process involving the rate constants of representative reactions within each subclass. Our work provides accurate rate constants and rate rules for this reaction class, which can aid in constructing more accurate combustion mechanisms for normal-alkyl cyclohexanes.
The application of reverse transcription quantitative real-time PCR technology for the production of gene tissue expression profiles is a widely employed approach in molecular biology research. It is ...imperative to ascertain internal reference genes that exhibit stable expression across diverse tissues to ensure the precision of tissue gene expression profiles. While there have been studies documenting the most suitable reference genes for various tissues in chickens, there is a dearth of research on the identification of reference genes in the gastrointestinal (GI) tract of chickens. This study utilized four different algorithms (Delt CT, BestKeeper, NormFinder, and Genorm) to assess the stability of 19 internal reference genes in various GI tract tissues, including individual GI tract tissues, the anterior and posterior GI tract, and the entire GI tissue. The RefFinder software was employed to comprehensively rank these genes. The research findings successfully identified the most appropriate internal reference genes for each type of GI tissue. Furthermore, HMBS, TBP, Ap2m, GUSB, DNAJC24, and RPL13 exhibited stable expression in the entire and posterior GI tract, whereas HMBS, TBP, Ap2m, GUSB, DNAJC24, and RPL13 demonstrated stable expression in the anterior GI tract. However, the internal reference genes commonly utilized, namely β-Actin, 18s RNA, and ALB, exhibit poor stability and are not advised for future investigations concerning gene expression in the GI region. Consequently, MUC2 and CDX1, two genes that specifically express in the gut, were chosen for examination to ascertain the stability of the aforementioned internal reference genes in this particular study. In summary, this study presents a relatively stable set of internal reference genes that can be employed to enhance the precision of quantifying mRNA expression levels in functional genes within the chicken GI tract.
Blade tip timing is an effective method for blade vibration measurements in turbomachinery. This method is increasing in popularity because it is non-intrusive and has several advantages over the ...conventional strain gauge method. Different kinds of sensors have been developed for blade tip timing, including optical, eddy current and capacitance sensors. However, these sensors are unsuitable in environments with contaminants or high temperatures. Microwave sensors offer a promising potential solution to overcome these limitations. In this article, a microwave sensor-based blade tip timing measurement system is proposed. A patch antenna probe is used to transmit and receive the microwave signals. The signal model and process method is analyzed. Zero intermediate frequency structure is employed to maintain timing accuracy and dynamic performance, and the received signal can also be used to measure tip clearance. The timing method uses the rising and falling edges of the signal and an auto-gain control circuit to reduce the effect of tip clearance change. To validate the accuracy of the system, it is compared experimentally with a fiber optic tip timing system. The results show that the microwave tip timing system achieves good accuracy.
Utilizing publicly available RNA-seq data to screen for ideal reference genes is more efficient and accurate than traditional methods. Previous studies have identified optimal reference genes in ...various chicken tissues, but none have specifically focused on the oviduct (including the infundibulum, magnum, isthmus, uterus, and vagina), which is crucial for egg production. Identifying stable reference genes in the oviduct is essential for improving research on gene expression levels. This study investigated genes with consistent expression patterns in the chicken oviduct, encompassing both individual oviduct tract tissues and the entire oviduct, by utilizing multiple RNA-seq datasets. The screening results revealed the discovery of 100 novel reference genes in each segment of oviduct tissues, primarily associated with cell cycle regulation and RNA binding. Moreover, the majority of housekeeping genes (HKGs) showed inconsistent expression levels across distinct samples, suggesting their lack of stability under varying conditions. The stability of the newly identified reference genes was assessed in comparison to previously validated stable reference genes in chicken oviduct and commonly utilized HKGs, employing traditional reference gene screening methods. HERPUD2, CSDE1, VPS35, PBRM1, LSM14A, and YWHAB were identified to be suitable novel reference gene for different parts of the oviduct. HERPUD2 and YWHAB were reliable for gene expression normalization throughout the oviduct tract. Furthermore, overexpression and interference assays in DF1 cells showed LSM14A and YWHAB play a crucial role in cell proliferation, highlighting the importance of these newly reference genes for further research. Overall, this study has expanded the options for reference genes in RT-qPCR experiments in different segments of the chicken oviduct and the entire oviduct.
In this paper, we show that if the equations
w
(
z
+
1
)
w
(
z
-
1
)
+
a
(
z
)
w
′
(
z
)
w
(
z
)
=
P
(
z
,
w
(
z
)
)
Q
(
z
,
w
(
z
)
)
,
and
(
w
(
z
)
w
(
z
+
1
)
-
1
)
(
w
(
z
)
w
(
z
-
1
)
-
1
)
+
...a
(
z
)
w
′
(
z
)
w
(
z
)
=
P
(
z
,
w
(
z
)
)
Q
(
z
,
w
(
z
)
)
,
where
a
(
z
) is rational,
P
(
z
,
w
) and
Q
(
z
,
w
) are coprime polynomials of
w
(
z
) with rational functions coefficients, have a non-rational meromorphic solution with hyper-order less than one, then the degrees of the numerator and denominator on the right sides of the equations have to meet certain conditions.
The long non-coding RNA (lncRNA) prostate cancer-associated ncRNA transcript 1 (
PCAT
-
1
) has been shown to promote prostate cancer cell proliferation through c-Myc and is associated with the poor ...prognosis of CRC patients. In the current study, it was hypothesized that the effect of
PCAT
-
1
on the aggressiveness of CRC cells was dependent on the function of c-Myc. Human CRC cell lines Caco-2 and HT-29 were transfected with specific
PCAT
-
1
shRNAs, and cell migration, invasiveness, and resistance to 5-fluorouracil were measured. To elucidate the role of c-Myc in
PCAT
-
1
function, c-Myc was overexpressed in
PCAT
-
1
-silenced CRC cells and the effect of c-Myc overexpression on the aggressiveness of
PCAT
-
1
-silenced cells was detected. The results showed that knockdown of
PCAT
-
1
in CRC cells suppressed cell motility and invasiveness, and sensitized the cells to 5-fluorouracil, as evidenced by the reduced viability and induced apoptosis in
PCAT
-
1
-silenced cells compared to the parental cells in response to 5-fluorouracil treatment. The expression of c-Myc in
PCAT
-
1
-silenced CRC cells was down-regulated, and forced expression of c-Myc partially restored the invasiveness in
PCAT
-
1
-silenced cells. In summary, the findings outlined in the current study suggest that
PCAT
-
1
regulates the invasiveness and drug resistance in CRC cells and that
PCAT
-
1
may promote CRC cell invasion by modulating the expression of c-Myc.
In this paper, we investigate uniqueness of finite-order transcendental meromorphic solutions of the following two equations:
and
where
is an irreducible rational function in
,
,
and
are small ...functions of
. Such solutions
are uniquely determined by their poles and the zeros of
(counting multiplicities) for two complex numbers
.
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