chore: remove redundant words

Signed-off-by: camcui <cuishua@sina.cn>

script/research/crypsinous/README.md

@@ -14,7 +14,7 @@ $(cm_{c_2},r_{c_2})=COMM(pk^{COIN}||\tau||v_c||\rho_{c_2})$,
 $\tau$ is the clock current time. \emph{$sn_c$} is the coin's serial number revealed to spend the coin.
 $$sn_c=PRF_{root_{sk}^{COIN}}^{sn}(\rho_c)$$
 $$\rho=\eta^{sk_{sl}^{COIN}}$$
-$\eta$ is is from random oracle evaluated at $(Nonce||\eta_{ep}||sl)$, $\rho$ is the following epoch's seed. $\emph{ptr}$ is the hash of the previous block, $\pi$ is the NIZK proof of the LEAD statement.
+$\eta$ is from random oracle evaluated at $(Nonce||\eta_{ep}||sl)$, $\rho$ is the following epoch's seed. $\emph{ptr}$ is the hash of the previous block, $\pi$ is the NIZK proof of the LEAD statement.
 
 ## st transactions
 the blockchain view is a chain of blocks, each block $B_j=(tx_{lead},st)$, while st being the merkle tree structure of the validated transactions received through the network, that include transfer, and public transactions.

script/research/crypsinous/ouroboros/ouroboros/clock.py

@@ -10,7 +10,7 @@ class SynchedNTPClock(object):
 
     def __init__(self, epoch_length, slot_length=60, ntp_server='europe.pool.ntp.org'):
         #TODO how long should be the slot length
-        self.epoch_length=epoch_length # how many slots in a a block
+        self.epoch_length=epoch_length # how many slots in a block
         self.slot_length=slot_length
         self.ntp_server = ntp_server
         self.ntp_client = ntplib.NTPClient()

script/research/homomorphic_encryption/README.md

@@ -42,7 +42,7 @@ $$sn_{c_i}=PRF_{root_{sk_{c_i}^{COIN}}}^{sn}(\rho_{c_i}), \forall_i \in \{1,2\}$
 
 ## homomorphic encryption mechanism
 
-spending the coin by nullifier defined as a poseidon hash of the secret key of the sender, and the serial number generated at random as such $H = PRF^{poseidon}(sk||sn)$ as a a proof of burn.
+spending the coin by nullifier defined as a poseidon hash of the secret key of the sender, and the serial number generated at random as such $H = PRF^{poseidon}(sk||sn)$ as a proof of burn.
 
 and the tx include encrypted note with the receipient public key
 ``` rust

src/sdk/src/crypto/merkle_node.rs

@@ -140,7 +140,7 @@ impl Hashable for MerkleNode {
     ///     - the root is at layer 0.
     /// `l` is MERKLE_DEPTH_ORCHARD - layer - 1.
     ///     - when hashing two leaves, we produce a node on the layer
-    ///       above the the leaves, i.e. layer = 31, l = 0
+    ///       above the leaves, i.e. layer = 31, l = 0
     ///     - when hashing to the final root, we produce the anchor
     ///       with layer = 0, l = 31.
     fn combine(altitude: Level, left: &Self, right: &Self) -> Self {